MHB Finding sum of infinite geometric series

[fluffertoes]

find the sum of this infinite geometric series:
1 - √2 + 2 - 2√2 + ...

a.) .414
b.) -2.414
c.) series diverges
d.) 2

I found that the common difference is 2, so I calculated this:

S_∞= -.414/-1
s_∞= .414

So i got that the answer is A, but will you check this?

 

[MarkFL]

In order for this to be a geometric series, we must have:

$$S=(1-\sqrt{2})\sum_{k=0}^{\infty}\left(a^k\right)$$

Going by the terms given, it appears that $a=2$, and so what does this tell us about the convergence?

 

[fluffertoes]

In order for this to be a geometric series, we must have:

$$S=(1-\sqrt{2})\sum_{k=0}^{\infty}\left(a^k\right)$$

Going by the terms given, it appears that $a=2$, and so what does this tell us about the convergence?

oh gosh i don't know

 

[MarkFL]

oh gosh i don't know

Recall that:

$$\sum_{k=0}^{\infty}r^k=\frac{1}{1-r}$$ but only if $|r|<1$

Otherwise, the sum diverges. :D

 

[fluffertoes]

Recall that:

$$\sum_{k=0}^{\infty}r^k=\frac{1}{1-r}$$ but only if $|r|<1$

Otherwise, the sum diverges. :D

But r stood to equal 2, so the answer should be c?

 

[fluffertoes]

but r stood to equal 2, so the answer should be c?

hello??

 

[MarkFL]

But r stood to equal 2, so the answer should be c?

Yes.

hello??

Sorry, but I was working on a coding request at vBorg. (Sweating)