If `n` is an even positive integer, then find the value of `x` if the greatest term in the expansion of `(1+x) ^n` may have the greatest coefficient also.

Find the limits between which x must lie in order that the greatest term in the expansion of (1+x)^30 may have the greatest coefficient.

Find the greatest term in the expansion of (a+x)^13, when a =5, x=2

If n is a positive integer then find the number of terms in the expansion of (x+y-2z)^(n)

If n is a positive integer then find the number of terms in the expansion of (x+y-2z)^(n)

The greatest coefficient in the expansion of (1+x)^(2n) is

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:The set al values of x for which thegreatest term in teh expnsionof (1+x)^30 may have the greatest coefficient is (A) (14/15, 15/14) (B) [15/16,16/15] (C) (15/16,16/15) (D) none of these

The greatest coefficient in the expansion of (1 + x)^(10) , is

Show that , if the greatest term in the expansion of (1 + x)^(2n) has also the greatest coefficient then x lies between (n)/(n +1) " and" (n+1)/(n)

If the sum of the coefficients in the expansion of (1 + 2x)^(n) is 6561 , then the greatest coefficients in the expansion, is

Write the coefficient of the middle term in the expansion of (1+x)^(2n) .