Home
Class 12
MATHS
The number of terms in the expansion of ...

The number of terms in the expansion of `(a+b+c)^n ,w h e r en in Ndot`

Text Solution

Verified by Experts

`(a+b+c)^(n) = [a+(b+c)]^(n)`
`=a^(n)+.^(n)C_(1)a^(n-1)(b+c)^(1) + .^(n)C_(2)a^(n-2)(b+c)^(2)+"….."+.^(n)C_(n) (b+c)^(n)`
Further, expanding each term of the R.H.S., we note that
First term consists of 1 term
Second term on simplification gives 2 terms
Third term on expansion gives 3 term
Fourth term on expansion gives 4 terms and so on.
`:.` Total number of terms `= 1 + 2 + 3 + "........" + (n+1)`
`= ((n+1)(n+2))/(2)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.1|17 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.2|10 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The number of terms in the expansion of (a + b + c)^(10) is

If the number of terms in the expansion of (x+y+z)^n are 36, then find the value of ndot

The number of terms in the expansion of [(a+b)^2]^(18) = ……………. .

The number of terms in the expansion of [(a+b)^2 ]^(18) = ………………….. .

If the coefficient of 4th term in the expansion of (a+b)^n is 56, then n is

If the middle term in the expansion of (x^2+1//x)^n is 924 x^6, then find the value of ndot

r and n are positive integers r gt 1 , n gt 2 and coefficient of (r + 2)^(th) term and 3r^(th) term in the expansion of (1 + x)^(2n) are equal, then n equals

If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w h e r en in Ndot

Find the largest term in the expansion of (3+2x)^(50),w h e r ex=1//5.

Statement 1: Greatest term in the expansion of (1+x)^(12),w h e nx=11//10 is 7th Statement 2: 7th term in the expansion of (1+x)^(12) has the factor ^12 C_6 which is greatest value of ^12 C_rdot