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Question

Let the sum of n terms of the series, 5+55+555+..... be Sn=5081(kn1)59n. Find k ?

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Solution

Let Sn=5+55+555+.............n terms
=5{1+11+111+....nterms}
=59{9+99+999+.....nterms}
=59{(101)+(1001)+(10001)+.....nterms}
=59{(10+100+1000+.....nterms)(1+1+1+......nterms)}
=59[10(10n1)101n]
=5081(10n1)59n

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