If the constant term in the binomial expansion of (x2−x1)n, n∈N is 15 then the value of n is equal to
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There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is2nCn−1.
Find the coefficient of x25
in expansion of expression r=0∑50(50)Cr(2x−3)r(2−x)50−r
Find the coefficient of x4
in the expansion of (1+x+x2+x3)11˙
Find the coefficient of x5 in (x+3)8
The number of terms in the expansion of (a+b+c)n,wheren∈N˙
If (2+3)n=I+f, whare I and n are positive integers and 0<f<1, show that I is an odd integer and (1−f)(1+f)=1
If the coefficient of the middle term in the expansion of (1+x)2n+2isα
and the coefficients of middle terms in the expansion of (1+x)2n+1
then relate α,βandγ˙
In the expansion of (1+x)n,
7th and 8th terms are equal. Find the value of (7/x+6)2