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प्रश्न
Compute the sum of first n terms of the following series:
6 + 66 + 666 + 6666 + ...
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उत्तर
Sn = 6 + 66 + 666 + ...... n terms
= 6[1 + 11 + 111 + ...... n terms]
= `6/9 [9 + 99 + 999 + ..... "n terms"]`
= `6/9[(10 - 1) + (10^2 - 1) + (10^3 - 1) + ... "n terms"]`
= `6/9[10 + 10^2 + 10 ^3 ..... "m terms" - (1 + 1 + 1 .... "n terms")]`
= `6/9[(10(10^"n" - 1))/(10 - 1) - "n"]`
= `6/9((10^"n" - 1)/9 - "n")`
= `6/9[(10(10^"n" - 1) - 9"n")/9 - "n"]`
= `6/81[10(10^"n" - 1) - 9"n"]`
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