If `1+2+3+…….+n = 36`, find the sum `1^3 + 2^3 +3^3+……….+n^3`.

If 1+2+3+……………+n=45, then 1^3+2^3+3^3+…………+n^3 is:

Prove the following by using the principle of mathematical induction for all n in N :- 1^3 + 2^3 + 3^3 + ... +n^3 =((n(n+1))/2)^2 .

Find the least value of n for which the sum 1 + 3 + 3^2 +...... to n terms is greater than 7000.

If "^(2n)C_3 : ^nC_2= 12: 1 , find n .

If n is an odd integer greater than or equal to 1, then the value of n^3 - (n-1)^3 + (n-2)^3 - (n-3)^3 + .... + (-1)^(n-1) 1^3

If sin A + cos A = m and sin^3 A + cos^3A=n , then (1) m^3-3m + n = 0 (2) n^3-3n + 2m=0 (3) m^3-3m + 2n = 0 (4) m3 + 3m + 2n = 0

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 2.3^2 + 3.3^3 +... + n.3^n =((2n-1)3^(n+1) +3)/4 .

Find the sum of n terms of the series 1. 2^2+2. 3^2+3. 4^2+

Find the value of n , if (2n - 1)/(n - 2) = 3