Advertisements
Advertisements
Question
In the binomial expansion of (a + b)n, if the coefficients of the 4th and 13th terms are equal then, find n
Advertisements
Solution
In (a + b)n general term is tr + 1 = nCr an – rbr
So, t4 = t3 + 1
= nC3
= nC12
⇒ n = 12 + 3
= 15
We are given that their coefficients are equal ⇒ nC3 = nC12
⇒ n = 12 + 3
= 15
[nCx = nCy ⇒ x = y (or) x + y = n]
APPEARS IN
RELATED QUESTIONS
Evaluate the following using binomial theorem:
(101)4
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Expand the following by using binomial theorem.
`(x + 1/x^2)^6`
Find the 5th term in the expansion of (x – 2y)13.
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the middle terms in the expansion of
`(2x^2 - 3/x^3)^10`
Find the term independent of x in the expansion of
`(x^2 - 2/(3x))^9`
Show that the middle term in the expansion of is (1 + x)2n is `(1*3*5...(2n - 1)2^nx^n)/(n!)`
Find the Co-efficient of x11 in the expansion of `(x + 2/x^2)^17`
The middle term in the expansion of `(x + 1/x)^10` is
Sum of the binomial coefficients is
Find the coefficient of x15 in `(x^2 + 1/x^3)^10`
Find the coefficient of x2 and the coefficient of x6 in `(x^2 -1/x^3)^6`
If n is a positive integer, using Binomial theorem, show that, 9n+1 − 8n − 9 is always divisible by 64
If n is a positive integer and r is a non-negative integer, prove that the coefficients of xr and xn−r in the expansion of (1 + x)n are equal
If the binomial coefficients of three consecutive terms in the expansion of (a + x)n are in the ratio 1 : 7 : 42, then find n
In the binomial expansion of (1 + x)n, the coefficients of the 5th, 6th and 7th terms are in AP. Find all values of n
Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is
