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Sum
Compute the sum of first n terms of the following series:
8 + 88 + 888 + 8888 + ...
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Solution
Sn = 8 + 88 + 888 + 8888 + ...... n terms
= 8[1 + 11 + 1111 + ...... n terms]
= `8/9 [9 + 99 + 999 + ..... "n terms"]`
= `8/9[(10 - 1) + (10^2 - 1) + (10^3 - 1) + ... "n terms"]`
= `8/9[10 + 10^2 + ... "m terms" - (1 + 1 + 1 .... "n terms")]`
= `8/9[(10(10^"n" - 1))/(10 - 1) - "n"]`
= `8/9[(10(10^"n" - 1))/9 - "n"]`
= `80/81(10^"n" - 1) - (8"n")/9`
Concept: Finite Series
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