If the number of terms in (1+x)^n be 11, find the 5th term and the val

1.	If the number of terms in (1+x)^n be 11, find the 5th term and the value of n
Answer» Given: In a binomial expression (1 + x)ⁿ, N = NUMBER of TERMS = 11 To find: 5TH TERM of the binomial expansion Solution: In a binomial expression (1 + x)ⁿ, nth term is defined by, $T=\binom{n}{r}(x)^{n-r}(1)^r$ n = Number of terms Therefore, 5th term of the given expression will be, $T=\binom{11}{4}(x)^{11-4}(1)^4$ $=\frac{11!}{(11-4)!4!}(x)^7$ $=\frac{11!}{(7)!4!}(x)^7$ $=\frac{11\times 10\times 9\times 8}{4\times 3\times 2\times 1}(x)^7$ = 330(x)⁷