If `t_r` is the rth term is the expansion of `(1+a)^n ` , in ascending power of a , prove that `r (r +1) t_(r+2) = (n - r + 1) (n - r) a^2 t_r`

If t_(r) denotes the rth term in the expansion (x+1/x)^(23) , and t_(12)=4t_(13) , then absx =_____

In a binomial expansion (x_y)^n gretest term means numericaly greatest term and therefore greatest term in (x-y)^n and (x+y)^n are ame. I frth therm t_r be the greatest term in the expansion of (x+y)^n whose therms are all ositive, then t_rget_(r+1) and t_rget_=(r-1)i.e. t_r/t_mge1 and t_r/t_(r-)ge1 On the basis of above information answer the following question:If rth term is the greatest term in the expansion f (2-3x0^10 then r= (A) 5 (B) 6 (C) 7 (D) none of these

Prove that .^(n-1)P_(r)+r.^(n-1)P_(r-1)=.^(n)P_(r)

In the expansion of (x+y)^(n),T_(r+1) = __________

Let n be a positive integer . If the cofficients of rth (r +1) th and (r +2)th terms in the expansion of (1 + x)^(n) are in AP, then find the relation between n and r .

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the expansion of (1 + x)^(1//4) are in AP, then r is /are

If the coefficients of a^(r-1),a^(r) and in the expansion of in the expansion of are in arithmetic progression,prove that n^(2)-n(4r+1)+4r^(2)-2=0