Question

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

Answer 1

Yes, this is a geometric series.
What is the common ratio, r? Is the absolute value of this r less than 1?
What is the formula for the sum of a geom. series when the first term and the common ratio r are known?

Answer 2

HI :DD

Answer 3

\[
\Large
\sum_{i=0}^k a r^i= \frac{a \left(1- r^{k+1}\right)}{1-r}

\]

Answer 4

If |r| < 1
\[

\Large
\sum_{i=0}^\infty a r^i= \frac{a }{1-r}
\]

Answer 5

Your a is 4 and your \( \Large r = -\frac 1 4 \)

Answer 6

Replace in the above formula and you are done.

Answer 7

i cant understand the formula probably becausse how its written

Answer 8

Read this
http://mathworld.wolfram.com/GeometricSeries.html

Answer 9

What is the choice C

Answer 10

16/5 is c

Answer 11

@eliassaab is it c?

Answer 12

Yes it is 16/5

Answer 13

thank you , could you help me with another please?

Answer 14

Post it as a new problem and tag me in it

Answer 15

just an alternative :
let A = 4 - 1 +1/4 - 1/16 + . . .
A = -4(-1 + 1/4 - 1/16 + . . .)

see if A = 4 - 1 +1/4 - 1/16 + . . .
then A - 4 = - 1 +1/4 - 1/16 + . . .

so,
A = -4 (A - 4)
A = -4A + 16
group them, get
5A = 16
A = 16/5

sometimes, algebraic is enjoy :)

Answer 16

thank you @RadEn

Answer 17

welcome :)