Show that the middle term in the expansion of (32x3+2x23)10 is 252
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If a and b are distinct integers, prove that a−b is a factor of an−bn, whenever n is a positive integer.
Let f(n)=k=1∑nk2(nCk)2, then the value of f(5) is equal to
If in the expansion of (1−x)2n−1 ardenotes the coefficient of xr then prove that ar−1+a2n−r=0
The co-efficient of x in the expansion of (1−2x3+3x5)(1+x1)8 is:
Find the expansion of (3x2−2ax+3a2)3
using binomial theorem.
Using Binomial Theorem, evaluate (102)5
Evaluate the following: (3+2)6−(3−2)6
Find the coefficient of x5 in the product (1+2x)6(1−x)7 using binomial theorem.