If the sum of the coefficients in the expansion of (q+r)20(1+(p−2)x)20 is equal to square of the sum of the coefficients in the expansion of [2rqx−(r+q)⋅y]10, where p, r,q are positive constants, then
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Find the term independent of x in the expansion of (x3+2x31)
Find the coefficient of x4
in the expansion of (2−x+3x2)6˙
be the coefficient of four consecutive terms in the expansion of (1+x)n,
then prove that: a1+a2a1+a3+a4a3=a2+a32a2˙
Using binomial theorem (without using the formula for nCr ) , prove that nC4+mC2−mC1nC2=mC4−m+nC1mC3+m+nC2mC2−m+nC3mC1+m+nC4˙
Prove that nC02nCn−nC12n−2Cn+nC22n−4Cn≡2n˙
Find the coefficient of x4 in the expansion of (2x−x23)10.
In the expansion of (1+x)50,
find the sum of coefficients of odd powers of x˙
Expand using Binomial Theorem (1+2x−x2)4,x=0.