## anonymous one year ago Find the sum of the infinite geometric series, if it exists. 4 - 1 +1/4 -1/16 + . . . A. - 1 B. 3 C. 16/5 D. does not exist

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1. anonymous

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2. anonymous

We have to find the common ratio since they told us this a geometric sequence. A common ratio (r) is basically the number divided by the preceding one. If we look at the sequence, we see that the common ration is -1/4 because: $(-1) / (4) = -1/4$ $(1/4)/(-1)= -1/4$ $(-1/16)/(1/4)= -1/4$ Now, there is a formula for finding the sum of an infinite geometric sequence. Basically, there is only one condition: $\Large \left| r \right|<1$ Or in other words $\Large -1<r<1$ r= -1/4 so it will work. The formula is $\Large Sum~of~a~geometric~sequence~(S_\infty)=$ $\Large \frac{ a_1 }{ 1-r }$ Where $\Large a_1=first~term$ $\Large r=~common~ratio$ Now plug in a_1= 4 and r= -1//4 in and tell me what you get

3. anonymous

Everywhere I said sequence, I meant series*

4. courtneygraley009

Use this math calculator to solve this geometric series. http://www.acalculator.com/quadratic-equation-calculator-formula-solver.html

5. Error1603

b