Find the term independent of x in the expansion of (2x - 1/x)^{10}

the second, third and fourth term of the binomial expansion (x+a)n (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)^{n} are in AP, then find values of n???

the coefficient of x^{4} in the expansion of (1+x+x^{2}+x^{3})^{11} is :

a) 900 b)909

c) 990 d)999

If 3rd,4th,5th,6th term in the expansion of (x+alpha)^{n} be respectively a,b,c and d, prove that b^{2}-ac/c^{2}-bd=4a/3c..

if 4th term in the expansion of ( ax+1/x)^{n }is 5/2, then the values of a and n :

a) 1/2,6 b) 1,3

c) 1/2,3

The coefficients of three consecutive terms in the expansion of(1+x)^{n} are in the ratio 1:7:42. find n.

Show that the middle term in the expansion of(1+x)raise to power 2n is = 1.3.5.......(2n-1) . 2n.xraise to power n upon n! , where nis a +ve integer.

Using Binomial theoram, prove that 2^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural number

solve this

if the coefficients of (r-5)^{th} and (2r-1)^{th} term in the expansion of (1+x)^{34} are equal, fiind r

using binomial therorem, 3^{2n+2}-8n-9 is divisible by 64, n belongs to N

Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

Find the term independent of x in the expansion of (2x - 1/x)

^{10}the second, third and fourth term of the binomial expansion (x+a)n (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

If the coeffients of 5th, 6th & 7th terms in expansion of (1+x)

^{n}are in AP, then find values of n???the coefficient of x

^{4}in the expansion of (1+x+x^{2}+x^{3})^{11}is :a) 900 b)909

c) 990 d)999

If 3rd,4th,5th,6th term in the expansion of (x+alpha)

^{n}be respectively a,b,c and d, prove that b^{2}-ac/c^{2}-bd=4a/3c..if 4th term in the expansion of ( ax+1/x)

^{n }is 5/2, then the values of a and n :a) 1/2,6 b) 1,3

c) 1/2,3

The coefficients of three consecutive terms in the expansion of(1+x)

^{n}are in the ratio 1:7:42. find n.Show that the middle term in the expansion of(1+x)raise to power 2n is = 1.3.5.......(2n-1) . 2n.xraise to power n upon n! , where nis a +ve integer.

Using Binomial theoram, prove that 2

^{3n }- 7n^{}-1 is divisible by 49 where n is a Natural numbersolve this

if the coefficients of (r-5)

^{th}and (2r-1)^{th}term in the expansion of (1+x)^{34}are equal, fiind r(1+2x+x^2)^20

^{3})((3/2)x^{2}- 1/3x)^{9.}using binomial therorem, 3

^{2n+2}-8n-9 is divisible by 64, n belongs to NFind the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn