Question

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

Answer 1

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

Answer 2

Answer:

210$x^{4}$

Step-by-step explanation: