Home
Class 12
MATHS
Find the sum of the coefficients of all ...

Find the sum of the coefficients of all the integral powers of `x` in the expansion of `(1+2sqrt(x))^(40)dot`

Text Solution

Verified by Experts

`(1+2sqrt(x))^(40) = .^(40)C_(0)+.^(40)C_(1)2sqrt(x)+"....."+.^(40)C_(40)(2sqrt(x))^(40)`
and `(1-2sqrt(x))^(40)=.^(40)C_(0)-.^(40)C_(1)2sqrt(x)+"....."+.^(40)C_(40)(2sqrt(x))^(40)`
`:. (1+2sqrt(x))^(40) + (1-2sqrt(x))^(40)`
`= 2[.^(40)C_(0) + .^(40)C_(2)(2sqrt(x))^(2)+"....."+.^(40)C_(40)(2sqrt(x))^(40)]`
Putting `x = 1`, we get
`.^(40)C_(0) + .^(40)C_(2)(2)^(2) + "...." + .^(40)C_(40)(2)^(40) = (3^(40)+1)/(2)`
`:.` Sum of all the integral powers of `x = (3^(40)+1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Example|10 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.1|17 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

Find the sum of the coefficients of integral powers of x in (1+3sqrtx)^20

The sum of the co-efficients of all the even powers of x in the expansion of (2x^2 - 3x + 1)^11 is -

The sum of coefficients of integral powers of x in the binomial expansion of (1-2sqrt(x))^(50) is: (1) 1/2(3^(50)+1) (2) 1/2(3^(50)) (3) 1/2(3^(50)-1) (4) 1/2(2^(50)+1)

Find the sum of the coefficient of to middle terms in the binomial expansion of (1+x)^(2n-1)

The sum of the coefficients of all even degree terms in x in the expansion of (x+sqrt(x^(3)-1))^(6)+(x-sqrt(x^(3)-1))^(6) , (xlt1) is equal to 4k. The value of k is ________

Find the sum of the coefficient of two middle terms in the binomial expansion of (1+x)^(2n-1)

The sum of the coefficients of middle terms in the expansion of (1+x)^(2n-1)

Find the coefficient of x^7 in the expansion of (x-1/(x^2))^(40) .

The coefficient of the middle term in the expansion of (1+x)^40 is

Find the sum of the coefficients of x^(32) and x^(-18) in the expansion of (2x^(3)-(3)/(x^(2)))^(14) .