if sum of the series a-(a+d)+(a+2d)-(a+3d)+ up to...........21 terms is
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upto to 20 terms in sum a get cancels , hence one a remains
hence
sum=a+d(1-2+3.............upto21 terms)
we according to bionomial theorem
(1+x)^-1=1-2x+3x^2-.........
if x=1
(1+1)^-1=1-2+3............+20)=2^-1=1/2
sum=a+d(1/2)
hence
sum=a+d(1-2+3.............upto21 terms)
we according to bionomial theorem
(1+x)^-1=1-2x+3x^2-.........
if x=1
(1+1)^-1=1-2+3............+20)=2^-1=1/2
sum=a+d(1/2)
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