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Question

If S=11+12+14+21+22+24+31+32+34......., then find the value of 14S.

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Solution

S=11+12+14+21+22+24+...S=n=1n1+n2+n4S=12n=12(n2+n+1)(n2n+1)S=12n=1(1(n2n+1)1(n2+n+1))S=12[(1113)+(1317)+(17113)+....]S=1214S=7

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