Calc help - Partial Sums?

Question

Can anyone help me with these??

1.) Let:

Sk = Summation from n=1 to k of n(0.1)^n

Find S3

2.) Determine the sum of the following series:

The Summation from n=1 to infinity of (-4^(n-1))/(8^n)

I have like 3 of each of these problems and I can't figure them out. My professor is horrible so please help!!

Answer 1

n=1 --> 1(.1)^1 = .1
n= 2 --> 2(.1)^2 = .02
n = 3 --> 3(.1)^3 = .003
Thus S3 = .1+.02+.003 = .123

(-4^(n-1))/(8^n)
= - 2 ^(2n-2)/ 2^3n
= -2^(2n-2-3n) = -2^(-2-n)
= 1/-2^(n+2) = -1/2^(n+2)
The 1st few terms are:
-1/8, - 1/16, -1/32 .....
So this is a geometric series with a = -1/8 and r = 1/2
The sum is -1/8(1/(1-1/2)) = - 1/4