Find the (r+1) -th term form the end in the expansion of `(1-3x)^(n)`

Find the (r+1)th term from the end in the expansion of (1-3x)^n .

Determine: (r+1)th term from the end in the expansion of (1-3x)^(n) .

Find the r^th term from the end in the expansion of (x + a)^n .

Find the fifth term form the end in the expansion of (sqrtx/3+2/5x)^11 .

5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

Ratio of the 5^(th) term from the beginning to the 5^(th) term from the end in the binomial expansion of (2^(1//3)+(1)/(2(3)^(1//3)))^(10) is

Find n, if the ratio of the fifth term from beginning to the fifth term from the end in the expansion of (root(4)(2) + 1/root(4)(3))^n id sqrt6:1 .

Find the fourth term in the expansion of (1-2x)^(3//2)""dot

Find n , if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (root(4)2 +1/(root(4)3 ))^n is sqrt(6): 1.

prove that the coefficient of the (r +1)th term in the expansion of (1+x)^(n) is equal to the sum of the coefficients of the rth and (r+1)th terms in the expansion of (1+x)^(n-1)