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## Homework Statement

Find the sequence of partial sums {S_n} and evaluate the limit of {S_n} for the following series

.9+.09+.009+...

What is .9+.09+.009+... equal to?

## Homework Equations

## The Attempt at a Solution

For the first part of the question (find the sequence of partial sums {S_n})

S_n=9(1/10)^n where n >= 1

my teachers assistant marked my answer correct

for the second part of the question (evaluate the limit of {S_n} for the following series .9+.09+.009+...)

I evaluated the limit of S_n by just simply taking the limit of S_n as n goes to infinity

lim n->inf S_n = 9*lim n->inf (1/10)^n = 0

My teachers assistant marked my question wrong and put

S_n = sigma[1,4] 9(1/10)^ character

I can't read what character he put

I don't see how this answer is correct and my answer is wrong. If my answer to finding S_n is correct then why can't I just evaluate the limit as n goes to infinity of S_n to "evaluate the limit of {S_n}? I don't understand what's wrong with my work.

for the third part (What is .9+.09+.009+... equal to?)

.9+.09+.009+... = sigma[n=1,inf] (1/10)^n = 9* (1/10)/(1-1/10) = 9* (1/10)/(9/10) = 9*1/10*10/9 = 1

my answer was marked correctly

I don't see how my answer to the second part is wrong. I hope somebody can clear up this confusion for me. Thanks for any help anyone can provide me.