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#1 2014-06-05 14:06:32

harrychess
Member
Registered: 2014-04-04
Posts: 33

Sequences

Let

Find the largest n so that

Compute the sum

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#2 2014-06-05 19:15:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2014-06-05 22:16:15

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,436
Website

Re: Sequences

For the first question, it might help you to consider the product f(n-1)f(n), and then the product f(n-2)f(n-1)f(n), f(n-3)f(n-2)f(n-1)f(n), etc... you should then get a neat formula for f(2)f(3)...f(n-1)f(n) which can be plugged into your inequality and solved for n.

Last edited by zetafunc (2014-06-05 22:22:10)

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#4 2014-06-07 22:51:33

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,996
Website

Re: Sequences

I need a by-hand solution for this.

The answer is 0.75 by the way

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#5 2014-06-08 00:40:37

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hi Agnishom

Solution

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#6 2014-06-08 00:44:07

Nehushtan
Member
Registered: 2013-03-09
Posts: 957

Re: Sequences

Agnishom wrote:

The series is undefined as the first term is
.

240 books currently added on Goodreads

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#7 2014-06-08 05:26:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Oh boy!

You meant:

telescope this to

and the answer follows.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2014-06-10 04:56:48

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,996
Website

Re: Sequences

Thank You;

How do I find these telescping formulae?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#9 2014-06-10 04:58:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Before asking that computational question, do you know what to do with the sums?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2014-06-10 05:02:14

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hi bobbym

Last edited by anonimnystefy (2014-06-10 05:02:44)

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#11 2014-06-10 05:06:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#12 2014-06-10 05:07:08

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hi

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#13 2014-06-10 05:09:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#14 2014-06-10 05:30:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hi bobbym

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#15 2014-06-10 05:38:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#16 2014-06-10 05:39:40

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hi

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#17 2014-06-10 05:40:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#18 2014-06-10 12:41:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,996
Website

Re: Sequences

bobbym wrote:

Before asking that computational question, do you know what to do with the sums?

Compute them, ofcourse?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#19 2014-06-10 17:56:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Do you know how to do it?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#20 2014-06-10 19:06:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,996
Website

Re: Sequences

Like ryagami did them?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#21 2014-06-10 22:07:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

Mine is a bit different than his.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#22 2014-06-10 23:36:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Hmm, how are they different?

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#23 2014-06-10 23:41:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

I just use a shift and the straight cancellation.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#24 2014-06-11 00:11:14

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Sequences

Well, I do that too, just a bit more rigorously.

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

#25 2014-06-11 00:13:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences

I was hoping to get him to see how the process works, why you even telescope at all. The simpler one is easier for me to explain.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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