Question -
Answer -
Given:
(1 + x)43
We know, thecoefficient of the r term in the expansion of (1 + x)n is nCr-1
So, the coefficientsof the (2r + 1) and (r + 2) terms in the given expansion are 43C2r+1-1 and 43Cr+2-1
For these coefficientsto be equal, we must have
43C2r+1-1 = 43Cr+2-1
43C2r = 43Cr+1
2r = r + 1 (or) 2r + r+ 1 = 43 [Since, nCr = nCs =>r = s (or) r + s = n]
2r – r = 1 (or) 3r + 1= 43
r = 1 (or) 3r = 43 – 1
r = 1 (or) 3r = 42
r = 1 (or) r = 42/3
r = 1 (or) r = 14
∴ r = 14 [since, value‘1’ gives the same term]