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Question

The sum of the series 7+77+777+........of n terms is .

A
781(10n+1109n]
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B
781(10n+1+109n]
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C
781(10n109n]
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D
781(10n+109n]
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Solution

The correct option is A 781(10n+1109n]
7+77+777+.......+to n terms=7(1+11+111+....+to n terms)=79(9+99+999+......+ to n terms)=79((101)+(1021)+(1031)+....+(10n1)]=79((10+102+103+....+10n)n]=79(10(10n1)101n]=781(10n+1109n].


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