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Question

Let S1 = nC0 + nC1 + nC2.............nCn and S2 = nC0 - nC1 + nC2 ..............+ (1)n nCn

Find the value of S1S1+S2 is ___.


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Solution

Consider the expansion of (1+x)n

(1+x)n=nC0+nC1x+nC2 x2+....+nCnxn

When we put x = 1, we get S1 and when we put x = -1, we get S2
S1=nC0+nC1+nC2 +....+nCn=2n
S2=nC0nC1+nC2 +....=0
S1S1+S2=S1S1=1


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