If the coefficients of x3and x4in the expansion of (1+ax+bx2)(1−2x)18in powers of x are both zero, then (a, b) is equal to
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Find the sum ∑0≤i<j≤n∑nCi
Find the sum C0−C2+C4−C6+,whereCr=∧6Cr=nCr
If the third term in the expansion of (1+x)mis−81x2,
then find the value of m˙
then find the value of a2+a4+a6++a12˙
Find the sum of the coefficients of all the integral powers of x
in the expansion of (1+2x)40˙
are positive integers and sk=1k+2k+3k++nk,
then prove that
Find the coefficient of xn
in the expansion of (1−9x+20x2)−1˙
Prove that α+β+γ=10∑α!β!γ!10!=310˙