Mathematics, 16.01.2020 02:31 kaylaamberd

What is the sum of the infinite geometric series? negative 3 minus three-halves minus three-fourths minus three-eighths minus three-sixteenths minus ellipsis

Answers: 3

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Answer from: kenisonpaigebosma

S=-6

Step-by-step explanation:

Sum Of A Geometric Series

Given a geometric series

$a_1,\ a_1.r,\ a_1.r^2,\ a_1.r^3,...$

The sum of the infinite terms is given by

$\displaystyle S_n=\frac{a_1}{1-r}$

The sum converges only if

|r|

We are given the series as a sum:

$S=\displaystyle -3-\frac{3}{2}-\frac{3}{4}-\frac{3}{8}-\frac{3}{16}...$

Factoring by -3:

$\displaystyle -3\left (1+ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}...\right )$

The expression in parentheses is a geometric series with

$a_1=1,\ r=1/2$

The sum can be computed by using the formula

$\displaystyle S_n=\frac{1}{1-1/2}$

S_n=2

So our expression becomes

S=(-3)(2)

$\boxed{S=-6}$

Answer from: Quest

use the power rule

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise

to the power of

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in ( x 2 ) 2

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply

2 by 2 . 9 x 4 ( y 3 ) 2

multiply the exponents in

( y 3 ) 2 .

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 4 y 3

⋅

multiply

3 by 2 . 9 x 4 y 6

step-by-step explanation:

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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