Home
Class 12
MATHS
Find the coefficient of x^k in1+(1+x)+(1...

Find the coefficient of `x^k in1+(1+x)+(1+x)^2++(1+x)^n(0lt=klt=n)dot`

Text Solution

Verified by Experts

The expansion being in G.P., we have
`E = 1 + (1+x) + (1+x)^(2)+"…….."+(1+x)^(n)`
`= ((1+x)^(n+1)-1)/((1+x)-1) = x^(-1)[(1+x)^(n+1)-1]`
Therefore, the coefficient of `x^(k)` in E is equal to the coefficient of `x^(k+1)` in`[(1+x)^(n+1)-1]`, which is given by ` .^(n+1)C_(k+1)`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Example|10 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.1|17 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

Find the coefficient of x^(18) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

The coefficient of x^n in the expansion of (1+x)(1-x)^n is

Find the coefficient of x^2 in (a/(a+x))^(1//2)+(a/(a-x))^(1//2)

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

If a_1, a_2 are the coefficients of x^n in the expansion of (1+x)^(2n) & (1+x)^(2n-1) respectively then a_1:a_2 will be

The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

Find the sum of coefficients in (1+x-3x^2)^(4163)dot

Find the coefficient of x^(r) in the expansion of (x+4)^(n)+(x+4)^(n-1)(x+3)+(x+4)^(n-2)(x+3)^(2)+.....+(x+3)^(n)