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Question

Sum of the series , 7+77+777+..... to n terms be S=(7m)(kn+1(k1)nk).Find mk1k ?

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Solution

7+77+777+...n=79[9+99+999+...n]

=79[(101)+(1021)+(1031)+...n]

=79[10+102+103+...n]79[1+1+1...n]

=79[10(10n1)101n]=79[10(10n1)9n]

=781[10n+1(10)9n]=781[10n+19n10]

m=81,k=10

mk1k=8110110=7010=7

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