## anonymous one year ago Identify whether the series summation of 15 open parentheses 4 close parentheses to the i minus 1 power from 1 to infinity is a convergent or divergent geometric series and find the sum, if possible.

1. anonymous

$\sum_{\infty}^{i=1}15(4)^i-1$

2. anonymous

It's suppose to be 15(4)^i=1

3. anonymous

This is a convergent geometric series. The sum is –5. This is a divergent geometric series. The sum is –5. This is a convergent geometric series. The sum cannot be found. This is a divergent geometric series. The sum cannot be found.

4. anonymous

I got A :)

5. jim_thompson5910

the exponent is i-1 ??

6. anonymous

Whether you meant $$5(4)^{i+1}$$ or $$5(4)^{i-1}$$, consider what happens as $$i\to\infty$$. $\lim_{i\to\infty}5(4)^{i}=\infty\neq0$ What do you know about series of the form $$\sum a_n$$ for which $$\lim\limits_{n\to\infty}a_n\neq0$$?

7. anonymous

Yes the exponent is i-1, and I think it's divergent

8. anonymous

That's right.

9. anonymous

And I couldnt find the sum so D!

10. jim_thompson5910

Yep whenever it's divergent, the infinite number of terms don't sum to one fixed number.