The sum of the series 7+77+777+........of n terms is .
A
781(10n+1−10−9n]
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B
781(10n+1+10−9n]
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C
781(10n−10−9n]
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D
781(10n+10−9n]
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Solution
The correct option is A781(10n+1−10−9n] 7+77+777+.......+tonterms=7(1+11+111+....+tonterms)=79(9+99+999+......+tonterms)=79((10−1)+(102−1)+(103−1)+....+(10n−1)]=79((10+102+103+....+10n)−n]=79(10(10n−1)10−1−n]=781(10n+1−10−9n].