# Multiplication of two series...

• June 27th 2010, 11:37 AM
Also sprach Zarathustra
Multiplication of two series...
Multiply these two series:

(1) $\Sigma^{\infty}_{n=1} \frac{1}{2^{n-1}}$

(2) $\Sigma^{\infty}_{n=1} \frac{1}{n\sqrt{n}}$
• June 27th 2010, 11:49 AM
mfetch22
Quote:

Originally Posted by Also sprach Zarathustra
Multiply these two series:

(1) $\Sigma^{\infty}_{n=1} \frac{1}{2^{n-1}}$

(2) $\Sigma^{\infty}_{n=1} \frac{1}{n\sqrt{n}}$

I believe the first series is equal to 2, correct? So wouldn't that imply that we just multiply each term in the second series by 2? I'm not certain, because I have no experience with multiplying infinite series, but wouldn't the result (since the first series is equal to 2) simply be:

$\Sigma^{\infty}_{n=1} \frac{2}{n\sqrt{n}}$

?
• June 27th 2010, 12:30 PM
Also sprach Zarathustra
Oooops...