Question

In an infinite gp series the first term is p and infinite sum is s then p belong to

Answer 1

p belongs to  0 < p < 2s

Given : An infinite GP series whose first term is p and sum is s.

To find: p belongs to

Solution:

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio

An Infinite GP series is,

x, xr, xr², −−−−∞

As given the first term is p, so our GP series becomes,

p , pr , pr² , ------- ∞

Sum of infinite GP series is given by,

S = first term / 1 – common ratio

S = p / 1-r

r = 1-p/s

Now since it is an infinite G.P. |r|<|, implies

–1 < 1 –p/s < 1 or

0 < p < 2s

#SPJ1