Which equation could be used to calculate the sum of geometric series? 1/3+2/9+4/27+8/81+16/243

Question

asked Mar 8, 2024 77.4k views

2 Answers

Greenkode · Answer 1 · 2024-03-10T03:01:57+0000

The sum of a geometric series can be calculated using the following equation:

S= (a(1-r^(n) ))/(1-r)

Where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio, and

n is the number of terms in the series.

In the given geometric series,
(1)/(3) + (2)/(9) + (4)/(27) +(8)/(81) +(16)/(243) ,

the first term, a =
(1)/(3) ,

the common ratio, r =
(2)/(3) ,

and the no. of terms,
n=5

Therefore using the equation, we can calculate the sum, S:

S= (1)/(3) ((1-((2)/(3))^(5) ))/(1-(2)/(3) )

Simplifying the equation gives:

or,
S= (1)/(3) ((1-(32)/(243)))/((1)/(3) )

or,
S= (1)/(3) (((211)/(243)))/((1)/(3) )

Therefore,
S= {(211)/(243)
Hence the sum of the given geometric series is
S= (211)/(243)}