Question

Find the sum of the series and explain how you know the sum converges to this value.
Sum of (((-1)^(n+1))/n) n=1, infinty.

Answer 1

\[\sum_{n=1}^{\infty} ((-1)^{n+1} x^n)/n \]

Answer 2

That's ln(1+x).

Answer 3

ln(1+1)=ln(2) but how you know it converges to this value?

Answer 4

Alternating series test.

Answer 5

Are you familiar with Taylor Series or Maclaurin Series?

Answer 6

yes

Answer 7

If you try to compute the Maclaurin series of:\[\ln(x+1)\]you will obtain the power series in your question.

Answer 8

differentiate the series...sun the then geometric series...integrate the series

Answer 9

*integrate the closed form after summing the geometric