<![CDATA[Math Is Fun Forum / Mathematical Induction]]> 2011-03-01T07:38:07Z FluxBB https://www.mathisfunforum.com/viewtopic.php?id=2984 <![CDATA[Re: Mathematical Induction]]> ganesh wrote:

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.

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https://www.mathisfunforum.com/profile.php?id=102287 2011-03-01T07:38:07Z https://www.mathisfunforum.com/viewtopic.php?pid=166570#p166570
<![CDATA[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)

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https://www.mathisfunforum.com/profile.php?id=5086 2006-09-23T02:48:14Z https://www.mathisfunforum.com/viewtopic.php?pid=42217#p42217
<![CDATA[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.

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https://www.mathisfunforum.com/profile.php?id=2128 2006-03-02T05:21:32Z https://www.mathisfunforum.com/viewtopic.php?pid=29540#p29540
<![CDATA[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.

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https://www.mathisfunforum.com/profile.php?id=682 2006-03-02T04:07:14Z https://www.mathisfunforum.com/viewtopic.php?pid=29530#p29530
<![CDATA[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).

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https://www.mathisfunforum.com/profile.php?id=2143 2006-03-01T18:01:55Z https://www.mathisfunforum.com/viewtopic.php?pid=29482#p29482
<![CDATA[Re: Mathematical Induction]]> I'm from Bulgaia. I can't tell you.

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https://www.mathisfunforum.com/profile.php?id=2128 2006-03-01T17:09:12Z https://www.mathisfunforum.com/viewtopic.php?pid=29475#p29475
<![CDATA[Re: Mathematical Induction]]> when did you learn?

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https://www.mathisfunforum.com/profile.php?id=2763 2006-03-01T17:03:04Z https://www.mathisfunforum.com/viewtopic.php?pid=29474#p29474
<![CDATA[Re: Mathematical Induction]]> OK.
I'll leave you to your maths teacher to teach you what's an integer.

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https://www.mathisfunforum.com/profile.php?id=2128 2006-03-01T17:00:53Z https://www.mathisfunforum.com/viewtopic.php?pid=29472#p29472
<![CDATA[Re: Mathematical Induction]]> sorry but I haven't even learnt what an integer is.

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https://www.mathisfunforum.com/profile.php?id=2763 2006-03-01T16:55:50Z https://www.mathisfunforum.com/viewtopic.php?pid=29470#p29470
<![CDATA[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

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https://www.mathisfunforum.com/profile.php?id=2128 2006-03-01T16:42:20Z https://www.mathisfunforum.com/viewtopic.php?pid=29469#p29469
<![CDATA[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.

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https://www.mathisfunforum.com/profile.php?id=2763 2006-03-01T16:39:10Z https://www.mathisfunforum.com/viewtopic.php?pid=29467#p29467
<![CDATA[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

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https://www.mathisfunforum.com/profile.php?id=2128 2006-02-28T06:11:19Z https://www.mathisfunforum.com/viewtopic.php?pid=29076#p29076
<![CDATA[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.

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https://www.mathisfunforum.com/profile.php?id=682 2006-02-28T04:48:15Z https://www.mathisfunforum.com/viewtopic.php?pid=29066#p29066