Question 1
By suitably manipulating the geometric series
=
, -1 < x < 1, you can calculate the sum of the series
. Use this method to evaluate the sum
.
◦ 6
◦ 10
◦ 8
◦ 4
◦ none of the above
Question 2
Using the known geometric series representation
=
x
n, valid for -1 < x < 1, find a power series representation for f(x) = ln(2 + x) in powers of x - 1. On what interval does the series converge to f(x)?
◦ f(x) = ln 3 +
n, for -2 < x ≤ 4
◦ f(x) = ln 2 +
n, for -1 < x < 3
◦ f(x) = ln 2 +
n, for -1 < x ≤ 3
◦ f(x) = ln 3 +
n, for -0 < x ≤ 2
◦ none of the above