Question

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.

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

I got A :)

Answer 5

the exponent is `i-1` ??

Answer 6

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 \(\lim\limits_{n\to\infty}a_n\neq0\)?

Answer 7

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

Answer 8

That's right.

Answer 9

And I couldnt find the sum so D!

Answer 10

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