The population of a local species of bees can be found using an infinite geometric series where a1 = 860 and the common ratio is one fifth. Write the sum in sigma notation and calculate the sum (if possible) that will be the upper limit of this population.

Question

anonymous · Answer

@SolomonZelman

solomonzelman · Answer

for how many terms?

anonymous · Answer

Not sure doesn't say, that's all the information provided

anonymous · Answer

@mathmale  Can you help? Solomon seems to of gotten offline.

mathmale · Answer

Hello!  Have you any previous experience with geometric series, and particularly with finding the sum of a geometric series when certain conditions are met?

anonymous · Answer

Somewhat, I've learned about it but never fully understood it. I'm taking a timed "exam" (they call it exam but it's mostly just an assigment with 15 questions) and I'm getting stumped.

mathmale · Answer

If r is the common ratio of a geometric series, and a is the first term of that series, a formula for the sum of that series (if and only if |r|<1 ) is given by$$\frac{ a }{  1-r}$$

mathmale · Answer

In the problem at hand, what is a?  what is r?  what is 1-r?  and, finally, what is a / (1-r)?

anonymous · Answer

a is 860? and r will be...the 1/5?

mathmale · Answer

That's right.  Go ahead and calculate the rest.

anonymous · Answer

I got 1, 075

mathmale · Answer

The "sum of a geometric series" is a limit, the limit that one reaches by summing up an infinite numberf of terms.   Your result represents such a limit here, and is correct.

anonymous · Answer

So would my response be \[\sum_{?}^{?} 860\left(\begin{matrix}1 \ 5\end{matrix}\right)^{i-1} the sum is 1, 075?

anonymous · Answer

Sorry, that came out wrong I'll try that again. $$\sum_{?}^{?} 860 \left(\begin{matrix}1 \ 5\end{matrix}\right) $$

mathmale · Answer

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