Question

why is there no infinite geometric series with a first term 10 and a sum 4?

Answer 1

I"m sure there is.

Answer 2

there isn't :( the problem asks you to explain why

Answer 3

Then, I don't know what I'm talking about.

Answer 4

@Callisto , @saifoo.khan , help pwease?

Answer 5

No idea.. sorry..
im stuck with "why" as well

Answer 6

I script kiddied wikipedia, and I know why now.

Answer 7

S=a/(1-r)

Answer 8

r must be less than 1, or it doesn't converge.

Answer 9

Assume it exists..
a
---- = Sum to infinity
1-r

10
---- = 4
1-r

10 = 4-4r
6= -4r
r= -3/2

However, for sum of infinity to exist, -1<r<1 . In this case, r=-3/2 < -1
So, it doesn't exist.
I don't know if this is correct though :(

Answer 10

S=4, and r=10

Answer 11

4-4r=10
6=-4r
r=-3/2

Answer 12

That's what wikipedia says, at least.

Answer 13

I just searched it in my dearest 'last minute' book :(

Answer 14

no that actually makes a ton of sense! thanks a lot guys!