Find the term:`n+(n-1)+(n-2)….+(r) terms`.

Find the sum of the following series up to the specified term n/n+(n-1)/n+(n-2)/n+ …..upto nth term.

Find the sum (1-1/n)+(1-2/n)+(1-3/n) +........upto n terms.

If the sum of the first n terms of an AP is 4n-n^2 ,what is the first term(that is S_1 )?What is the sum of first two terms?What is the second term?Similarly,find the 3rd,the 10th and nth terms.

Prove that: n(n-1)(n-2)…..(n-r+1)=(n!)/((n-r)!)

The sum of n terms of two arithmetic progressions aree in the ratio (5n+4):(9n+6) .Find the ratio of their 18th terms.

In a G.P., the (p + q)th term is m and (p-q)th term is n. Find its pth term.

Find the rth term of an A.P., the sum of whose first n terms is 2n+3n^2 .

The nth term of a sequence is given by 2^(n+1)/3^n . Prove that it is a geometric sequence. Also find the first term and common ratio of it.

The pth term of an A.P. is —q and qth term is -p. If the nth term is zero, find n.

Find the indicated terms of the sequence whose nth terms are a_n=(-1)^(n-1) a_3,a_9 .