Let the smallest value of k, for which the coefficient of x³ in (1+x)³+(1+x)⁴+(1+x)⁵+ +(1+x)⁹⁹+(1+kx)¹⁰⁰, x≠0, is (43n+101/4)(¹⁰⁰C₃) for some n, be p. Then the value of p+n is:

Binomial Theorem and Its Simple Applications: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Morning shift · Q9

JEE Main 20264 Apr, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let the smallest value of

k\in\mathbb{N}

, for which the coefficient of

x^3

(1+x)^3+(1+x)^4+(1+x)^5+\dots+(1+x)^{99}+(1+kx)^{100}

x\ne0

, is

\left(43n+\frac{101}{4}\right)\left({}^{100}C_3\right)

for some

n\in\mathbb{N}

, be

p

. Then the value of

p+n

is: