Question

If the sum of an Infinite G.P. is . Whose terms are decreasing and first then is 5, then Belongs to a)(5,infinity) b)(5/2,infinity)-{5} c)(-5/2,5/2) d)(0,5/2)

Answer 1

Given : An infinite GP with first term = 5  and decreasing

To find :   sum of an Infinite G.P. Belongs to a)(5,infinity) b)(5/2,infinity)-{5} c)(-5/2,5/2) d)(0,5/2)

Solution:

Infinite  GP

a  = 5

0 <  r < 1

Sum of infinite Series =  a/(1 - r)

= 5/(1 - r)

Case 1  :  

r → 0

$\lim_{r \to o} \frac{5}{1-r}$

= 5/(1 - 0)

= 5/1

= 5

Case 1  :  

r → 1

$\lim_{r \to 1} \frac{5}{1-r}$ =

= 5/(1 - 1)

= 5/0

= Infinity

sum of an Infinite G.P. Belongs to (5,infinity)    

option a is correct

Learn more:

In an infinite g.P. Each term is equal to three times the sum of all the ...

https://brainly.in/question/9079152

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

https://brainly.in/question/12999165