confusion with geometric series (1 Viewer)

[Pace_T]

hey all
for sum of geometical series
there's two formulas right
is it |r|<1 and |r|>1
or r>1 and r<1
becoz when i look in some books it's got the absolute values while others dont.
then when i look at this question;

1 - rt2 + 2 ...

etc
the sum of first 10 terms is correct when i use the formula with 1-r^n etc (not r^n -1 etc) (i tested it by adding the 10 terms separately in the calculator)

but the r value is -1.41...
so wouldn't that be |r|>1
so im drawn 2 the conclusion that it's the latter set of conditions (r>1, r<1) and not the absolute values one.
right?
cheers.

 

[FinalFantasy]

there's S_n=a(r^n-1)\(r-1)
or S_n=a(1-r^n)\(1-r)

the bottom has to be similar

 

[goan_crazy]

|r|<1
because -1<r<1
For a limiting sum, it has to be between -1 and 1

 

[switchblade87]

Even if you use the wrong formula, won't you have - / - (negative over negative) anyway, so that they cancel out?

 

[acmilan]

Either form can be used correctly

 

[adambra]

Even if you use the wrong formula, won't you have - / - (negative over negative) anyway, so that they cancel out?

Yes. .

 

[switchblade87]

Yes. .

In other words, whatever formula you chuck it into, it will work out to be the same answer...I dunno, I'm probably wrong

 

[MarsBarz]

I'm assuming that you are not talking about the limiting sum of a geometric serie, just simple geometric sums.
The proof for the sum of geo series is simple. Learn it. You'll realise that the absolute value thing is just out there to confuse you and is redundant. Both sum formulae produce the same results with any input as they are essentially the same.

 

[switchblade87]

I'm assuming that you are not talking about the limiting sum of a geometric serie, just simple geometric sums.
The proof for the sum of geo series is simple. Learn it. You'll realise that the absolute value thing is just out there to confuse you and is redundant. Both sum formulae produce the same results with any input as they are essentially the same.

Thats what I said!