Trouble summing $\frac{1}{3^i}$ from 1 to n

Question

$\sum_{i=1}^n \frac{1}{3^i}\tag{displayed}$

I can't figure this out. I expanded it: $(\frac {1}{3^1}+\frac{1}{3^2}+...+\frac{1}{3^n})=S$, and I think the technique is to multiply both sides by something and then subtract, but I'm not quite sure how to make everything cancel out. Any hints would be appreciated.

Multiply both sides by $3$. Then note the left hand side of the resulting equation is $1+S-{1\over 3^n}$. Then solve for $S$. — David Mitra, Apr 03 '13 at 14:36

score 1 · Accepted Answer · answered Apr 03 '13 at 14:32

1

Hint: Do you know the geometric series?

answered Apr 03 '13 at 14:32

Dominic Michaelis

19,935

@Rokko Nevermind that, I feel the same often enough. If this helped you, you can upvote or accept :) – Dominic Michaelis Apr 03 '13 at 14:38

score 1 · Answer 2 · answered Apr 03 '13 at 14:39

1

In geometric progression a(1st term)=1/3 and r=1/3 so sum= a(r^n -1)/r-1

answered Apr 03 '13 at 14:39

pallavi

11

Welcome to MSE! It really helps to format answers using MathJax (see FAQ). Regards – Amzoti Apr 03 '13 at 15:06
+1 As you are a new user and this is your first post! :). – hrkrshnn Apr 03 '13 at 15:29

score 0 · Answer 3 · answered Apr 03 '13 at 14:47

0

step 1. Multiply the left hand and right hand the equation you post by 1/3. Mark it as b_n(the origin one is a_n)

step 2. calculate a_n - b_n

it is what you want.

answered Apr 03 '13 at 14:47

user70794

1

Trouble summing $\frac{1}{3^i}$ from 1 to n

3 Answers3