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

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)

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:

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

Therefore,

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:

link

The answer to your question would be 360 cm squared :)