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Question
Find the sum of the following series up to n terms:
5 + 55 + 555 + …
Sum
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Solution
S = 5 + 55 + 555 + ….. up to n terms
= `5/9 [9 + 99 + 999 + ...... "up to n terms"]`
= `5/9 [(10 - 1) + (100 - 1) + (1000 - 1) +... "up to n terms"]`
= `5/9 [(10 + 100 + 1000 + ...... "up to n terms") - (1 + 1 + ...."to n terms")]`
= `5/9[(10(10^"n" - 1))/(10 -1) - "n"]`
= `5/9[(10(10^"n" - 1))/9 - "n"]`
= `50/81 [10^"n" - 1] - (5"n")/9`
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