Question -
Answer -
It is known that (r +1)th term, (Tr+1), in the binomialexpansion of (a + b)n is givenby 
.
Assuming that xn occursin the (r + 1)th term of the expansion of (1+ x)2n, we obtain
Comparing the indices of x in xn andin Tr + 1, we obtain
r = n
Therefore, the coefficient of xn inthe expansion of (1 + x)2n is
Assuming that xn occursin the (k +1)th term of the expansion (1 + x)2n –1, we obtain
Comparing the indices of x in xn and Tk +1, we obtain
k = n
Therefore, the coefficient of xn inthe expansion of (1 + x)2n –1 is
From (1) and (2), it is observedthat
Therefore, the coefficientof xn in the expansion of (1 + x)2n istwice the coefficient of xn in the expansion of (1+ x)2n–1.
Hence, proved.