The sum of all the coefficients of the terms in the expansion of (x+y+z+w)6 which contain x but not y, is
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Find the value of ∑0≤i≤j≤n∑(i+j)(nCi+nCj)˙
Show that 9n+1−8n−9
is divisible by 64, where n
is a positive integer.
The number of terms in the expansion of (1+x)101(1+x2−x)100 in powers of x is
If the 3rd, 4th , 5th and 6th term in the expansion of (x+α)n
be, respectively, a,b,candd,
prove that c2−bdb2−ac=3c5a˙
Find the coefficient of x4 in the expansion of (2x−x23)10.
Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (42+431)n is 6:1.
In the expansion of (1+x)50,
find the sum of coefficients of odd powers of x˙
Show that the coefficient of the middle term in the expansion of (1+x)2nis equal to the sum of the coefficients of two middle terms in the expansion of (1+x)2n−1.