alexwing285
contestada

Which equation represents the partial sum of the geometric series?
A. 125+25+5+1
B. 25+5+1+1/5
C. 1+1/5+1/25+1/125
D. 1/125+1/5+5+125

Which equation represents the partial sum of the geometric series A 1252551 B 255115 C 1151251125 D 1125155125 class=

Respuesta :

irspow
The geometric sequence after the sigma is 125(1/5)^(n-1) so the first four terms are

125, 25, 5, and 1

So A is the sum of the first four terms...

The more common formula for the sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=term number

With the more specific infinite sum if r^2<1 as n approaches infinity

s=a/(1-r)
ankitprmr2

The partial sum of the geometrical series is 125+25+5+1. Thus, option (A) is correct.

The sum of geometric series given in the question can be represented as:

[tex]S_n={\sum}_{n=1}^{4} (125)\left( \dfrac{1}{5} \right)^{n-1}[/tex]

Now, put the values of n from 1 to 4 to find the terms geometric series.

Therefore,

[tex]\begin{aligned}S_1&=(125)\left( \dfrac{1}{5} \right)^{1-1}\\&=125 \end{aligned}[/tex]

[tex]\begin{aligned}S_2&=(125)\left( \dfrac{1}{5} \right)^{2-1}\\&=125 \times \dfrac{1}{5}\\&=25\end{aligned}[/tex]

[tex]\begin{aligned}S_3&=(125)\left( \dfrac{1}{5} \right)^{3-1}\\&=125 \times \dfrac{1}{25}\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}S_4&=(125)\left( \dfrac{1}{5} \right)^{4-1}\\&=125 \times \dfrac{1}{125}\\&=1\end{aligned}[/tex]

Hence, the partial sum of the geometrical series is 125+25+5+1. Thus, option (A) is correct.

To know more about the Geometric Series, please refer to the link:

https://brainly.com/question/21087466

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