Tagged Questions
1
vote
1answer
278 views
Proof of 2nd Derivative of a Sum of a Geometric Series
I am trying to prove how $$g''(r)=\sum\limits_{k=2}^\infty ak(k-1)r^{k-2}=0+0+2a+6ar+\cdots=\dfrac{2a}{(1-r)^3}=2a(1-r)^{-3}$$
or $\sum ak(k-1)r^(k-1) = 2a(1-r)^{-3}$.
I don't know what I am doing ...
1
vote
0answers
69 views
geometric sum with probabilities
I have the following sum to consider:
$$
p_i/(1+r)^i
$$
for i = 1 to 10
My question is, whether this can be somehow evaluated using some sort of mathematical insight without explicitly computing ...
