Home
Class 12
MATHS
Let m be the smallest positive integer s...

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 the value of n is

Text Solution

AI Generated Solution

To solve the problem, we need to find the smallest positive integer \( m \) such that the coefficient of \( x^2 \) in the expansion of \[ (1+x)^2 + (1+x)^3 + (1+x)^4 + \ldots + (1+x)^{49} + (1+mx)^{50} \] is equal to \( (3n + 1) \cdot \binom{51}{3} \) for some positive integer \( n \). ...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Numerical|25 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(n) in the expansion of (1)/((1-x)(3 -x)) , is

The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3)) , is

If n is a positive integer, find the coefficient of x^(-1) in the expansion of (1+x)^n(1+1/x)^ndot

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

The sum of the coefficients in the expansion of (1 - x + x^(2) - x^(3))^(n) ,is

The smallest natural number n, such that the coefficient of x in the expansion of (x^(2) + (1)/(x^(3)))^(n) is .^(n)C_(23) , is

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

If |x| lt 1 , then the coefficient of x^n in expansion of (1+x+x^2 + x^3 +…….)^2 is

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio