Question

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

Answer 1

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

Answer 2

Everywhere I said sequence, I meant series*

Answer 3

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

Answer 4

b