Can you pls solve this question quickly in detail :-
Show that the middle term in the expansion of (1+x) 2n is
[{1*3*5...(2n-1)} /n! ] *2n xn
Please solve this quickly.....................
Middle term will be the ( (2n/2) +1 )th = ( n + 1 )th
- Tn+1 = 2nCn * ( 1 )2n-n * ( x )n
- = (2n)! / [ n! * n! ]
- = (2n)(2n-1)(2n-2)...(2)(1) / [ (n)(n-1)(n-2)...(2)(1) n!] * xn
- = (2n-1)(2n-3)...(3)(1) * { 2(n) * 2(n-1)...2(1)} / [ n(n-1)(n-2)(n-3)...(1) * n! ] * xn
- = 2n * (2n-1)(2n-3)(2n-5)...(1) / n! * xn
- = 1 * 3 * 5 * 7....(2n-1) / n! * 2n * xn
HENCE PROVED.
Good Question.
