Math CentralQuandaries & Queries


Question from Kalyani, a student:

sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is?

A person who really understands what is going on would realize that 9 = 8.99999... and would be able to guess the final digit in the sum up to eight terms. If you are not such a person, then you have to work a bit. You are told that for some starting point x, the infinite sum

x + x/10 + x/100 + ...

equals 9. So factor out the x to get

x(1 + 1/10 + 1/100 + ...) = (1.111...)x = (10/9)x,

and set 10x/9 = 9. Now solve for x. Your task is to add the first eight terms, x + x/10 + ... + x/10000000.


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