If the third term in expansion of (1+xlog2x)5 is 2560 then x is equal to (a) 22 (b) 81 (c) 41 (d) 42
If xp occurs in the expansion of (x2+1/x)2n , prove that its coefficient is [31(4n−p)]![31(2n+p)]!(2n)! .
Let S1=0≤i<j≤100∑∑CiCj, S2=0≤j<i≤100∑∑CiCj and S3=0≤i=j≤100∑∑CiCj where Cr represents cofficient of xr in the binomial expansion of (1+x)100
If S1+S2+S3=ab where a, b∈N, then the least value of (a+b) is
If N is a prime number which divides S=39P19+38P19+37P19+…+20P19, then the largest possible value of N among following is
Consider a G.P. with first term (1+x)n, ∣x∣<1, common ratio 21+x and number of terms (n+1). Let ′S′ be sum of all the terms of the G.P., then
The coefficient of xn is ′S′ is