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 x⁴ in the expansion of (1+x+x²+x³)¹¹ is :

a) 900 b)909

c) 990 d)999

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 2³ⁿ - 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, 3²ⁿ⁺²-8n-9 is divisible by 64, n belongs to N

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

if three successive coefficients in the expressions of (1+x)ⁿ are 220, 495 and 792 respectively, find the value of n?

Find a, b and n in the expansion of (a + b)ⁿ if the first three terms of the expansion are 729, 7290 and 30375, respectively.

the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of

Find the sixth term of the expansion (y^1/2 + x^1/3)ⁿ, if the binomial coefficient of the third term from the end is 45.

The cofficient of three consecutive terms in the expansion of (1+x)ⁿare in the ratio 1:7:42.find n?

1. find the coefficient of x^-17 on the expansion of (x⁴-1/x³)^15..
2. find the term independent of x in the expansion of(1/2x^1/3+x^-1/5)8.
3. find the coefficient of x⁸ *y16 in the expansion of (x+y)^18.

 if C1, C2, c3, C4 are the coefficient of 2nd, 3rd , 4th , and 5th , term in the expansion of (1+x)raise to "n" then prove that

C1/C1+c2  + c3/c3+c4 = 2c2/c2+c3     ((((((((((((((((((((( where c1+c2 , c3 +c4 and c2 + c3 are together under the division  THAT IS C1 BY C1 +C2 etc.))))))))))))

The sum of the coefficients of the first three terms in the expansion of (x-3/x²)^m , x is not equal to 0,m being a natural number, is 559. Find the term of the wxpansion containing x³. (NCERT PG 174 EXAMPLE NO 16). The steps in the NCERTbook are not clear..

The 3rd, 4th and 5th terms in the expansion of (x + a)n are respectively 84, 280 and 560, find the values of x, a and n.

the coefficients of 2nd, third and fourth terms in the expansion of (1+n)^2n are in AP.Prove that 2n^2-9n+7=0

in the binomial expansion of (a + b)ⁿ , the coefficient of the 4th and the 13th terms are equal to each other. find n?

This is my doubt:

Find a if the coefficients of x² and x³ in the expansion of (3+ax)⁹ are equal.

Thanks a lot. =)

The sum of two numbers is 6 times their geometric mean show that the numbers are in the ratio (3+2.2^1/2):(3-2.2^1/2)

Show that 2⁴ⁿ-15n-1 is divisible by 225 by using binomial theorem.

Find the fifth term from the end in the expansion of (x³/2 - 2/x²)⁹

using binomial theorem prove that  6ⁿ-5n always remender -1when divided by 25

any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

SOLVE

1) C1+2C2+3C3+--------+nCn=n2 to power n-1

please give the blueprint of annual examination of maths paper.

if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x.

If the coefficient of x^r in the expansion of (1-x)^2n-1 is denoted by a_r then prove that a_r-1 + a_2n-r = 0.

The no of irrational terms in the expansion of (4^1/5 + 7^1/10)⁴⁵ are??????

Find the coefficient of x⁵⁰  in the expansion :

(1+x)¹⁰⁰⁰ + 2x(1+x)⁹⁹⁹ +3x²(1+x)⁹⁹⁸+…………………..+1001x¹⁰⁰⁰

The first 3 terms in the expansion of (1+ax)ⁿ are 1, 12x, 64x²respectively, Find n and 'a' .