Infinite Series

Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.

The sum of an infinite G.P. is 15 and the sum of the squares of these terms is 45. Find the G.P.

The sum of first two terms of an infinite G.P. is 15 and each term is equal to the sum of all the terms following it. Find the G.P.

The first term of a G.P. exceeds the second term by 2 and the sum to infinity is 50. Find the G.P.

Find the values of p,if sum to infinity for the G.P. p,1,1/p,.....is25/4.

One side of an equilateral triangle is 18 cm. The mid points of its sides are joined to form another triangle whose mid-points are joined again to form another triangle. This process is repeated infinitely. Find the sum of the perimeters of all the triangles.