Reimann Sum Problems?

Question

Hey guys, I have been having trouble with the following types of problems and was wondering if I could get a couple solutions.

1. Let |p|<1

SUM of (i*p^i)
(1
2. 1. Let |p|<1

SUM of ((i^2 )*(p^i))
(1

Answer 1

1.
The sum converges to
p / (p - 1)^2

2.
The sum converges to
-(p^2 + p) / (p - 1)^3

Answer 2

you mustn't get the comparable answer. once you employ reimann sums you the two a an decrease than estimate or an over estimate. So in the experience that your answer is as on the brink of the fundamental as accessible then you definately are suitable. i think of you're applying the E thingymajiggy. (5/3)x^3+3x^2+x is the fundamental.