If there are (2n+1) terms in an A.P., then prove that the ratio of the sum of odd terms to the sum of even terms is (n+1) : n

Find the sum of n terms of the series whose nth term is : 2^(n-1)-1 .

Find the sum to n terms of the A.P. whose kth term is 5k + 1.

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.

Find the sum to n terms of the A.P., whose k^(th) term is 5k+ 1 .

Find the sum of n terms of the series whose nth terms is (i) n(n-1)(n+1) .

Find the sum to n terms of the series whose nth term is n^(2) + 2^(n) .

If the 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

Find the sum of n terms of the series whose nth term is given by n^2+2^n

Find the sum of n terms of the series whose nth terms is (ii) n^(2)+3^(n) .

Find the sum of first n terms of an A.P. whose nth term is 3n+1.