Question

Help, will give medal

What is the smallest integer that can possibly be the sum of an infinite geometric series whose first term is 9?

Answer 1

@SithsAndGiggles @misty1212

Answer 2

the sum to infinity of a Geometric series is a1 / (1 - r)
where a1 = first term and r is common ratio ( r < 1)

Answer 3

uh... you mean a_1?

Answer 4

a_1 if you like - doesnt really matter
in this case its 9

Answer 5

ok so the sum is 1-r
and actually isnt it -1<r<1

Answer 6

I'm not sure how to do this to be honest
one guess would be when r = 0.1 making the sum = 9/.9 = 10

Answer 7

yes it should be -1 < r < 1

Answer 8

the sum is a_1 / (1 -r)

Answer 9

if r = -0.5 then Sum = 9 / 1-(-0.5) = 9 / 1.5 = 6

thats lower still

Answer 10

what we require is the highest negative number that will divide into 9 exactly -
so we have to look at values of 1 - r where r is between -1 and 0
what if r = -0.8 then sum = 9 / (1.8) = 5

Answer 11

I think thats it

Answer 12

I don't think there is another number between 1.8 and 2 that gives an integer when you divide it into 9