Prove that

I am thinking something like that :

and since we get

Am i right?

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- Jan 25th 2011, 03:30 AMSENTINEL4Proving Limit
Prove that

I am thinking something like that :

and since we get

Am i right? - Jan 25th 2011, 03:43 AMProve It
What value are you making approach?

- Jan 25th 2011, 03:49 AMSENTINEL4
- Jan 25th 2011, 04:38 AMthemekanikal
- Jan 25th 2011, 06:00 AMHallsofIvy
Just because a term "goes to 0", that does't mean you can ignore it in the sum. Its values for finite n are NOT 0 and will affect the sum. For example, 1/n goes to 0 but goes to infinity.

- Jan 25th 2011, 06:49 AMSENTINEL4
Which is the correct method to reach to the answer then?

- Jan 25th 2011, 07:04 AMProve It
I don't think this limit does go to ...

The limit of a sum is the sum of the limits, and if you evaluate the limit of each term using L'Hospital's Rule, you should find each term .

So the limit should be ... - Jan 25th 2011, 07:08 AMSENTINEL4
- Jan 25th 2011, 09:09 AMchisigma
The problem is to find [if it exists...] the limit of the sequence...

(1)

It is evident from (1) that, because is the sum of n positive terms and for all k is for all n will be . But for all k is also...

(2)

... so that...

(3)

The first ten are...

Kind regards

- Jan 25th 2011, 10:18 AMFernandoRevilla
If is the limit of (the given sequence) we have:

Equivalently:

Taking limits:

which implies .

Fernando Revilla - Jan 25th 2011, 11:06 AMFernandoRevilla

Here the result is not valid because the number of terms of depends on .

Fernando Revilla - Jan 25th 2011, 10:50 PMthemekanikal