Question

calculate the first 30 partial sums for:

A)1- 1/2 + 1/3 - 1/4 + 1/5 -...
B) 1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + 1/9 +1/11 - 1/6 +...
C)1 + 1/3 + 1/5 - 1/2 + 1/7 + 1/9 + 1/11 - 1/4 +...

Then estimate what A and B converge to and estimate the error.

Answer 1

All of your series A, B and C are the MacLaurin series expansion for ln(1 +x), where x = 1. You are just doing the summation in a different order.

The exact sum for the infinite series is ln(2) = 0.69315...

I don't see the point of adding up 30 terms in different orders, but if that is what they want you to do, do it.