# Math Help - FInding the sum

1. ## FInding the sum

Hi, how can one find the sum of the series:
for the sequence such that:

Is it some series?
Thanks.

2. ## Re: FInding the sum

Originally Posted by pranay
Hi, how can one find the sum of the series:
for the sequence such that:

Is it some series?
Thanks.
I don't fully understand your question, but maybe this would be helpful.

$S_n(x)=\sum^n_{k=1}a_kx^k$

$S_n$ is clearly $S_n(1)$.

Now, the derivative of $S_n(x)$ is:

$(S_n(x))'=(\sum^n_{k=1}a_kx^k)'=\sum^n_{k=1}ka_kx^ {k-1}$.

So $(S_n(1))'=\sum^n_{k=1}ka_k$.

3. ## Re: FInding the sum

You can find $a_{n+1}$ writing $(n+1)a_{n+1} = \sum_{k=1}^{n+1}ka_k -\sum_{k=1}^nka_k$.

4. ## Re: FInding the sum

the value of S(2) and S(5) is
0.70833333333 and
0.73809523810 respectively . So how can one relate to calculating the differentiation?
Thanks.