Question

How to find summation formula when denominator and numerator both have an series?

Answer 1

To find the sum of the above infinite geometric series, first check if the sum exists by using the value of . Here the value of is . Since | 1 2 | < 1 , the sum exits. Now use the formula for the sum of an infinite geometric series.

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Answer 2

∑j=0n10−j10+j∑j=0n10−j10+j

=−∑j=0nj+10−2010+j=−∑j=0nj+10−2010+j

=−∑j=0nj+1010+j+∑j=0n2010+j=−∑j=0nj+1010+j+∑j=0n2010+j

=−(n+1)+20(∑j=1n+101j−∑j=1
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hope it helps you ☺

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