Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2006-02-27 16:48:15
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Mathematical Induction
MI # 1
Prove that the sum of n terms of
1*1! + 2*2! + 3.3! + 4*4!+.....n*(n+1)!
is (n+1)!-1.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#2 2006-02-27 18:11:19
- krassi_holmz
- Real Member
- Registered: 2005-12-02
- Posts: 1,905
Re: Mathematical Induction
k.k!= (k+1)k! - k! = (k+1)! - k!
so
1.1!+2.2!+3.3!+4.4!+...+(n).(n)!/*not n+1*/=2!-1!+3!-2!+4!-3!+...+(n+1)!-n!= (n+1)!-1
Last edited by krassi_holmz (2006-02-27 18:14:10)
IPBLE: Increasing Performance By Lowering Expectations.
Offline
#3 2006-03-01 04:39:10
- espeon
- Real Member
- Registered: 2006-02-05
- Posts: 2,586
Re: Mathematical Induction
I have no idea what those numbers say or mean.Probably because we haven't learn't about whatever you're talking about yet.
Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Offline
#4 2006-03-01 04:42:20
- krassi_holmz
- Real Member
- Registered: 2005-12-02
- Posts: 1,905
Re: Mathematical Induction
It's never early to learn something:
k! means the product of all positive integers, less or equal to k:
k!=1.2.3. ... .k
Last edited by krassi_holmz (2006-03-01 05:00:39)
IPBLE: Increasing Performance By Lowering Expectations.
Offline
#5 2006-03-01 04:55:50
- espeon
- Real Member
- Registered: 2006-02-05
- Posts: 2,586
Re: Mathematical Induction
sorry but I haven't even learnt what an integer is.
Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Offline
#6 2006-03-01 05:00:53
- krassi_holmz
- Real Member
- Registered: 2005-12-02
- Posts: 1,905
Re: Mathematical Induction
OK.
I'll leave you to your maths teacher to teach you what's an integer.
IPBLE: Increasing Performance By Lowering Expectations.
Offline
#7 2006-03-01 05:03:04
- espeon
- Real Member
- Registered: 2006-02-05
- Posts: 2,586
Re: Mathematical Induction
when did you learn?
Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Offline
#8 2006-03-01 05:09:12
- krassi_holmz
- Real Member
- Registered: 2005-12-02
- Posts: 1,905
Re: Mathematical Induction
I'm from Bulgaia. I can't tell you.
IPBLE: Increasing Performance By Lowering Expectations.
Offline
#9 2006-03-01 06:01:55
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Mathematical Induction
The differences between integers, rationals, and reals don't really have to be well defined (bad pun...) to understand them. Just think of an integer as any whole number, without a decimal or fraction, a ration is anything that can be put in the form a/b (where a and b are integers), and real includes all the numbers without a complex part (i).
Last edited by Ricky (2006-03-01 06:02:27)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
#10 2006-03-01 16:07:14
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Mathematical Induction
krassi_holmz, I am not able to understand your proof. If no other member posts the solution, I shall do it before posting the next problem.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
#11 2006-03-01 17:21:32
- krassi_holmz
- Real Member
- Registered: 2005-12-02
- Posts: 1,905
Re: Mathematical Induction
I'm expressing kk! of the form f(k+1)-f(k) so the sum
When I do this all f-s between 2 and n reduct as you see because f(k) thakes part in f(k+1)-f(k) with sign "-" and in f(k)-f(k-1) whit sign "+".
So there left only -f(1) and +f(n+1):
Now it's not hard to prove that kk!= (k+1)!-k!:
(k+1)!-k!= ((k+1)k!)-k!=k!(k+1-1)=kk!
so for every k kk!= (k+1)!-k!=f(k+1)-f(k),where f(x)=x!
So the sum:
,
which have to be proven.
Last edited by krassi_holmz (2006-03-01 17:24:50)
IPBLE: Increasing Performance By Lowering Expectations.
Offline
#12 2006-09-22 14:48:14
- mapu
- Member
- Registered: 2006-09-22
- Posts: 1
Re: Mathematical Induction
CAn you help me with a question about mathematical induction?
Prove that
k^4= (k^5)/5 + (k^4)/2 +(K^3)/3 -k/30
by mathematical induction for the next term (k+1)
Offline
#13 2011-02-28 19:38:07
- G-man
- Member
- Registered: 2011-02-28
- Posts: 16
Re: Mathematical Induction
MI # 1
Prove that the sum of n terms of
1*1! + 2*2! + 3.3! + 4*4!+.....n*(n+1)!
is (n+1)!-1.
You wrote n=1 instead of n
Let f(n)donate the series (|Last term is n*n!).
The statement is true for some p.
Maths!......
Offline
Pages: 1