The sum to infinity of the series    is

a) 3

b) 4

c) 6

d) 2

Let f(x) be a polynomial function of second degree. If f (1) = f (−1) and a, b, c are in arithmetic progression then  and  are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) Arithmetic – Geometric Progression

 is equal to

a) 1

b) –1

c) 0

d) None of these

If  are the sums of  terms respectively of an arithmetic progression show that .

In an arithmetic progression of which a is the first term, if the sum of the first p terms = 0, show that the sum of the next q terms is equal to

Find an arithmetic progression whose first term is unity such that the second, tenth and thirty fourth sums form a geometric progression.

The sum of four numbers in arithmetic progression is 48 and the product of their extremes is to the product of their means as 27 to 35. Find the numbers.

Show that
 

The arithmetic mean between m and n and the geometric mean between a and b are each equal to   ; find m and n in terms of a and b.

If x, y, z are in harmonic progression show that
 

Find the value of the infinite series
 

Find the generating function, the sum to n terms and the n^th term of the recurring series

Find the sum of the first n terms of the series whose r^th term is
 

Find the sum to infinity of the series whose n^th term is
 

Find the sum of the series
6, 24, 60, 120, 210, 336, . . . . . . to n terms.

Find the sum of the series
 to infinity

Sum to n terms
 

Sum to n terms, the series 1, 6, 15, 28,  .  .  .  .  .

Sum the series
 

Sum the series
6 + 9 + 14 + 23 + 40 + .  .  .  .  .  to n terms

Sum the series
 to n terms

Sum of the series
 to infinity

Sum of the series