Last one I'm stuck on:

$\displaystyle a_n$ = ?

{ $\displaystyle 1, -\frac{2}{3}, .4444444444444444, - .296296296296296296,.....$}

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- Mar 15th 2009, 09:54 PMmollymcf2009Another infinite sequence
Last one I'm stuck on:

$\displaystyle a_n$ = ?

{ $\displaystyle 1, -\frac{2}{3}, .4444444444444444, - .296296296296296296,.....$} - Mar 15th 2009, 09:57 PMmatheagle
- Mar 15th 2009, 10:07 PMADARSH
- Mar 15th 2009, 10:13 PMADARSH
Here is the explanation about third and 4th term

$\displaystyle x = .4444444444444444.. ---> (1)$

$\displaystyle 10x = 4.44444...----->(2)$

(2) - (1)

$\displaystyle 9x= 4 $

$\displaystyle

x = \frac{4}{9} = \frac{ 2\times 2}{ 3 \times 3} $

$\displaystyle x = -0.296296296296296296 ..---> (1) $

$\displaystyle 1000x =- 296.296296......----> (2)$

(2)-(1)

$\displaystyle 999x = -296 $

$\displaystyle x = \frac{-296}{999} = \frac{4 \times \not 37 \times -2}{9 \times \not 37 \times 3 }$ - Mar 15th 2009, 10:17 PMmatheagle
That's way too much work 4 me.

I just used my calculator to check (2/3) to the third power.

The first three are obvious.