Question -
Answer -
Given:
(1 + x)18
We know, thecoefficient of the r term in the expansion of (1 + x)n is nCr-1
So, the coefficientsof the (2r + 4) and (r – 2) terms in the given expansion are 18C2r+4-1 and 18Cr-2-1
For these coefficientsto be equal, we must have
18C2r+4-1 = 18Cr-2-1
18C2r+3 = 18Cr-3
2r + 3 = r – 3 (or) 2r+ 3 + r – 3 = 18 [Since, nCr = nCs =>r = s (or) r + s = n]
2r – r = -3 – 3 (or)3r = 18 – 3 + 3
r = -6 (or) 3r = 18
r = -6 (or) r = 18/3
r = -6 (or) r = 6
∴ r = 6 [since, rshould be a positive integer.]