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Question

S1=12+16+112+120+
S2=13+152+133+154+135+156+If S12S2=a12, then a=
  1. 0.5    
  2. 1    
  3. 2   
  4. 2.5    


Solution

The correct option is C 2   
S1=12+16+112+120+=n=11n(n+1)=n=1(1n1n+1)=limn(1112)+(1213)+(1314)++(1n1n+1)=limn(11n+1)S1=1limn1n+1=1

S2=13+152+133+154+135+156+=(13+133+135+)+(152+154+156+)=131132+1521152=38+124=512S12S2=12×512=212a=2

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