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Question

The sum of 312(12)+423(12)2+534(12)3+ upto 20 terms is

A
1121(12)20
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B
1+121(12)20
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C
1120(12)21
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D
1+120(12)21
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Solution

The correct option is A 1121(12)20
Given : Sn=312(12)+423(12)2+534(12)3+S20=20n=1n+2n(n+1)(12)nS20=20n=12(n+1)nn(n+1)(12)nS20=20n=1[1n(12)n11n+1(12)n]S20=112(12) +12(12)13(12)2 +13(12)214(12)3 +120(12)19121(12)20S20=1121(12)20

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