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Question Number 855 by 112358 last updated on 26/Mar/15
Findthenumberoftermsin(1+x)101(1+x2−x)100.
Answered by prakash jain last updated on 26/Mar/15
=[(1+x)(1+x2−x)]100(1+x)=[1+x2−x+x+x3−x2]100(1+x)=[1+x3]100(1+x)=(1+x3)100+x(1+x3)300(1+x3)100=∑100i=0100Cix3i(101terms)...(i)x(1+x3)100=∑100i=0100Cix3i+1(101terms)...(ii)Totalnumberofterms=202sincenocommontermsin(i)and(ii).
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