If a, b, c, d be `3^(rd), 4^(th), 5^(th) and 6^(th)` terms of the expansion of `(p+q)^(n)`, where n is a positive integer prove that `(b^(2)-ac)/(c^(2)-b)=(5a)/(3c)`.

If a_(1), a_(2), a_(3), a_(4) are the coefficients of the 2^(nd), 3^(rd), 4^(th) and 5^(th) terms respectively in the binomial expansion of (1+x)^(n) where n is a positive integer prove that (a_(1))/(a_(1)+a_(2)) , (a_(2))/(a_(2)+a_(3)) , (a_(3))/(a_(3)+a_(4)) are in arithmetic progression.

The (n+1)th term in the expansion of e^(-3x) is

The (n+1)th term in the expansion of e^(-2) is

Prove that : Find the 5^("th") term in the expansion of (3x-4y)^(7) .

The 3^(rd), 4^(th), 5^(th) terms in the expansion of log_(e )2 are respectively a, b, c then their ascending order is

If the coefficient of (3r)^(th) and (r + 2)^(th) terms in the expansion of (1 + x)^(2n) are equal then n =

The number of terms in the expansion of (a+b+c+d)^5 is

If the coefficient of rth, (r + 1)th and (r+ 2)th terms in the expansion of (1 + x) ^(n) are respectively in the ratio 2:4:5, then (r,n)=