The number of terms in the expansion of (a + b + c)n, where n ∈ N is

Question

The number of terms in the expansion of (a + b + c)n, where n ∈ N is (A) ((n+1)(n+2)/2) (B) n + 1 (C) n + 2 (D) ( n + 1)n/2

Tardigrade Admin · Accepted Answer

We have, ( a + b + c)n = [ a + (b + c)]n = an+ nC1 an-1(b+c)1+ nC2 an-2(b+c)2+... ... + nCn(b+c)n Further, expanding each term of R.H.S., we note that first term consist of 1 term. Second term on simplification gives 2 terms. Third term on simplification gives 3 terms and so on. ∴ The total number of terms = 1 + 2 + 3 + ... + (n + 1) = ((n+1)(n+2)/2)

Q. The number of terms in the expansion of $(a + b + c)^{n}$ , where $n \in N$ is

$\frac{( n + 1 ) ( n + 2 )}{2}$

$n + 1$

$n + 2$

$(n + 1) n /2$

Q. The number of terms in the expansion of (a+b+c)n, where n∈N is

2(n+1)(n+2)​

n+1

n+2

(n+1)n/2

Q. The number of terms in the expansion of $(a + b + c)^{n}$ , where $n \in N$ is

$\frac{( n + 1 ) ( n + 2 )}{2}$

$n + 1$

$n + 2$

$(n + 1) n /2$