If (1+x)n=C0+C1x+C2x2+.....+Cnxn then prove that
C0/1 - C1/22 + C2/32 - C3/42+.....+(-1)nCn/(n+1)2
=1/(n+1) [1+(1/2)+(1/3)+.....(1/(n+1))]
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1 Answers
62(1+x)n=ΣCrxr
integrate wrt x
(1+x)n+1/(n+1)=ΣCrxr+1/(r+1)
now divide by x on both sides and integrate again..
(1+x)n+1/x(n+1)=ΣCrxr/(r+1)
(1+x)n+2/x(n+1)(n+2)+(1+x)n+2lnx/(n+1)=ΣCrxr+1/(r+1)2
putting x=-1.. i get 0 on the LHS.. and -RHS!!!
Is there some mistake that i am making?!!!