SOLUTION: What is the sum of (2/3) + (2/3)^2 + (2/3)^3 + (2/3)^4 +....+ (2/3)^100 ? I think the answer is 2-2(2/3)^100

Algebra ->  Sequences-and-series -> SOLUTION: What is the sum of (2/3) + (2/3)^2 + (2/3)^3 + (2/3)^4 +....+ (2/3)^100 ? I think the answer is 2-2(2/3)^100       Log On


   

Question 972087: What is the sum of (2/3) + (2/3)^2 + (2/3)^3 + (2/3)^4 +....+ (2/3)^100 ?
I think the answer is 2-2(2/3)^100

Answer by farohw(175) About Me  (Show Source):
You can put this solution on YOUR website!

Hello,

Using the rule %28p%2Fq%29%5En+=++p%5En%2Fq%5En we have (2/3)^n
where n represents the exponents 1, 2, 3, 4, +... +, 100. So for,



The sum of (2/3) + (2/3)^2 + (2/3)^3 + (2/3)^4 +....+ (2/3)^100 will be as follows:



and the decimal approximation is 1.99999...

Your answer 2-2(2/3)^100 is correct.