Question
How can I sketch a graph of the first two partial sums for the following power series:
Sum(n=1 to infinity) ((2x+5)^n) / (n(4^n))
Sum(n=1 to infinity) ((2x+5)^n) / (n(4^n))
Answers
Steve
just plot the graphs:
n=1: (2x+5)/4
n=2: (4x^2+36x+65)/32
http://www.wolframalpha.com/input/?i=plot+(2x%2B5)%2F4,+(4x%5E2%2B36x%2B65)%2F32
Notice they both cross the x-axis at x = -5/2
n=1: (2x+5)/4
n=2: (4x^2+36x+65)/32
http://www.wolframalpha.com/input/?i=plot+(2x%2B5)%2F4,+(4x%5E2%2B36x%2B65)%2F32
Notice they both cross the x-axis at x = -5/2