Question

What is the sum of infinite geometric series when the first term is 4 and ratio=3/4?

Answer 1

It'd be approaching 0 very closely as we add them.

Answer 2

Well, maybe we could say 0.

Answer 3

4/(1- 3/4)
=16

Answer 4

@binary3i it is 3/4 not -3/4

Answer 5

@binary3i what happened to (3/4) raised to infinity?

Answer 6

sum of an infinite GP with common ratio r
is a(1-r^n)/(1-r)
here n is infinite and r is 3/4 which is smaller than one which causes
r^n to vanish, it becomes smaller and smaller.

Answer 7

here a is 4

Answer 8

@binary3i thanks but what if r is 4/3? I know that r^n becomes bigger and bigger

Answer 9

Yes, it will.

Answer 10

what is it square of .1?
it is .01
so here you see that square is smaller than that number.
the numbers smaller than 1 when raised to high powers they become smaller and smaller. 1 raised to any power remains 1.
And numbers greater than 1 when raised to high power become bigger and bigger.