Pls help sum of the series
1/2 - 1/2(1/2)^2 + 1/3(1/2)^3 - 1/4(1/2)^4 + .....

Question

Pls help sum of the series
1/2 - 1/2(1/2)^2 + 1/3(1/2)^3 - 1/4(1/2)^4 + .....

anonymous · Answer

$$\sum_{n=1}^{\infty}$$(-1)^n 1/(2n)^n

anonymous · Answer

make that (-1)^n+1

anonymous · Answer

I dont have any idea about series, pls be more specific

anonymous · Answer

this is an alternating series. You can tell by the way that its going from positive to negative. To find the sum you need to find it to the nth term.

anonymous · Answer

thats where the sum I placed in the first comment is the sum to the nth term. What I would want to know is if you're trying to find if its convergent or divergent?

anonymous · Answer

i dont have any clue about series so i cant understand it :(

anonymous · Answer

whats the directions asking?

anonymous · Answer

the sum of that series, is the first comment the formula or the answer?

anonymous · Answer

thats the formula

anonymous · Answer

how can i add in the nth term?

anonymous · Answer

its ln(3/2)