Calc-Find value of Maclaurin series of f(x) at a point?

Question

The series is a value of the Maclaurin series of a function f(x) at a particluar point. What function and what point? What is the sum of the series?

(-1)^N(1/4^n)

(-1)^n-1[(2^n)/(n3^n)]

Answer 1

1) 1-1/4+1/16 = 1-x+x^2-x^3+ = 1/(1+x) at x=-1/4 sum =4/5
summing from n=0
If I understand your writing this is
(-1)^n *(2/3)^n/n summing from n=1
-ln(1+x)=-x+x^2/2-x^3/3+.. at x= 2/3
sum= -ln(1+(2/3)) =-ln(5/3)