# Math Help - Series Problem

1. ## Series Problem

I am having trouble to adding up

1 + 100/99.9 + 100/99.8 + 100/99.7 + .....+ 100/0.1

More generally,

1 + 1/(1-a) + 1/(1-2a) + 1/(1-3a) + ..... + 1/(1-ka)

My brain cells are dying very quickly, any help would be appreciated.

(I apologize if this is in the wrong section, I'm not sure where Series should go)

2. Originally Posted by yyhow
I am having trouble to adding up

1 + 100/99.9 + 100/99.8 + 100/99.7 + .....+ 100/0.1

More generally,

1 + 1/(1-a) + 1/(1-2a) + 1/(1-3a) + ..... + 1/(1-ka)

My brain cells are dying very quickly, any help would be appreciated.

(I apologize if this is in the wrong section, I'm not sure where Series should go)
Start be defining $u=0.1$, then your series is:

$S=100/u+100/(2u)+ ... + 100/(1000u)=\frac{100}{u}(1+1/2+1/3+...+1/1000)=\frac{100}{u}H_{1000}$

where $H_n$ is the $n$-th harmonic number, and $H_{1000}\approx 7.485$

CB