Thread: geometric series

Hello,

Originally Posted by kithy

given the geometric series s(x) = the sum from n=1 to infinity of (-e^-x)^n.

a) set x=1 in the above series and write out the first 4 terms
b) find the exact sum of the series s(1)
c) fing the exact sum of the series s(x)
d) for what values of x does the series from part (c) converge?

for part A i set the S(1) = the sum from n=1 to infinity of (-1/e)^n, and i think i got the first 4 terms but i still don't know what it converges to.

You're not asked that... Your series is right.

so on part B i got a sum of s(1) = e/(e+1) is it right?

Right

on part C i got S(x) = e^x/(e^x+1) right?

Only if (else, the series diverges), so it's for x>0 (this is part D).

Actually, the exact value of s(x) is : (simplify it the way you want)

since i am not sure about my answers i don't know part D, for what values it converges.

You can use the alternate series test

Hi

Originally Posted by kithy

given the geometric series s(x) = the sum from n=1 to infinity of (-e^-x)^n.
so on part B i got a sum of s(1) = e/(e+1) is it right?

on part C i got S(x) = e^x/(e^x+1) right?

I don't agree.

is negative because it's an alternating series and so can't be true.

You may try rewriting the series as :

Ow, this is the mistake :

The sum of terms of a geometric series is that thing, multiplied by the first term.
Here, the first term is

Hence,

sorry about that