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denpristay [2]
3 years ago
14

What is the sum of the geometric series

Mathematics
2 answers:
elena55 [62]3 years ago
8 0

When it isn't rounded the answer is:

2.67

Once rounded to the nearest whole number the answer is:

3

lbvjy [14]3 years ago
4 0
If S denotes the sum of the first n terms of a geometric series with first term a and common ratio r, then

S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}
rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n
\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n
\implies (1-r)S=a(1-r^n)
\implies S=a=\dfrac{1-r^n}{1-r}

Using summation notation, you have

S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}

In this case, you have a=2, r=\dfrac12, and n=16. So the value of the sum is

\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67

Rounded to the nearest whole number, the answer would be 3.
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A piece of string that is 9.4 meters long is cut into two pieces. One piece is 3 times as long as the other. Find the length of
xenn [34]

9.4=3x+x

9.4=4x

=2.35

the shorter piece is 2.35 and <u>the longer piece is </u><u>7.05</u>

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3 years ago
Given a right triangle, If tan aq=3/4, what is the length of the side adjacent to aq?
olasank [31]
Tan = o/a and = 3/4 so the opposite is 3 and the adjacent is 4
8 0
3 years ago
PLEASE HELP ASAP ILL REALLY APPRECIATE IT
sesenic [268]

Answer:

see below

Step-by-step explanation:

2.5 = 2 5/10 = 250%

40% = .40 = 40/100 = 4/10 =2/5

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1/4 = 25/100 = 25%

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3 0
3 years ago
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PLEASE HELP ASAAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Nutka1998 [239]

Let i = sqrt(-1) which is the conventional notation to set up an imaginary number

The idea is to break up the radicand, aka stuff under the square root, to simplify

sqrt(-8) = sqrt(-1*4*2)

sqrt(-8) = sqrt(-1)*sqrt(4)*sqrt(2)

sqrt(-8) = i*2*sqrt(2)

sqrt(-8) = 2i*sqrt(2)

<h3>Answer is choice A</h3>
5 0
3 years ago
Find the point at which the line joining the two points (-3,-5) and (7,5) cuts they y axis
8090 [49]

Answer:

(0,-2)

Step-by-step explanation:

First we find the equation of the line passes through (-3,-5) and (7,5).

The slope of the line is

m=\frac{5-(-5)}{7-(-3)}\\=\frac{10}{10}\\=1

So by the point slope formula the equation of the line is

y-5=1(x-7)\\y=x-7+5\\y=x-2

When x=0 we have y=0-2=-2.

Therefore the line joining the two points cuts the y-axis at (0,-2).

4 0
2 years ago
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