Question -
Answer -
Given:
(1 +┬аx)43
We know, thecoefficient of the r term in the expansion of (1 + x)n┬аis┬аnCr-1
So, the coefficientsof the (2r + 1) and (r + 2) terms in the given expansion are┬а43C2r+1-1┬аand┬а43Cr+2-1
For these coefficientsto be equal, we must have
43C2r+1-1┬а=┬а43Cr+2-1
43C2r┬а=┬а43Cr+1
2r = r + 1 (or) 2r + r+ 1 = 43 [Since,┬аnCr┬а=┬аnCs┬а=>r = s (or) r + s = n]
2r тАУ r = 1 (or) 3r + 1= 43
r = 1 (or) 3r = 43 тАУ 1
r = 1 (or) 3r = 42
r = 1 (or) r = 42/3
r = 1 (or) r = 14
тИ┤ r = 14 [since, valueтАШ1тАЩ gives the same term]