Solve Infinite Summation Homework Statement

[chinchins]

Homework Statement

"A notation that you may find helpful in this task is the factorial notation n!, defined by
n!=n(n-1)(n-2)….3 x 1 x 1 e.g. n!=5 x 4 x 3 x 2 x 1(=120) Note that 0!=1

Consider the following sequence of terms where x = 1 and a = 2.
1, ((ln2))/1, ((ln2)^2 )/(2 x 1), ((ln2)^3)/(3 x 2 x 1) ….

Calculate the sum S_n of the first n terms of the above sequence for 0≤n≤10. Give your answers correct to six decimal places."

How do i solve this? My teacher gave this to us without telling us what to do or any way of solving it. Can u help me solve this?
I tried searching the net, scanned my book but i could not find any part which could help me. this is my first time tackling a math problem like this and i have no clue on solving it. thanks

 

[vela]

What's there to solve? The problem just asks you to calculate some sums.

 

[chinchins]

uhm i don't know wer to start calculating for the problem :(

 

[vela]

If you have a sequence {a_n}, you can form a new sequence:

$$\begin{align*} S_0 &= a_0 \\ S_1 &= a_0+a_1 \\ S_2 &= a_0+a_1+a_2 \\ &\vdots \\ S_n &= a_0+\cdots+a_n \end{align*}$$

The S_n's are called partial sums. The problem is asking you to calculate the first 11 sums for the given sequence.

 

[chinchins]

i see... its only the first part of the question though and there's more.. but thanks for the help!