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adelina 88 [10]
3 years ago
14

Which equation could be used to calculate the sum of the geometric series? One-third + two-ninths + StartFraction 4 Over 27 EndF

raction + StartFraction 8 Over 81 EndFraction + StartFraction 16 Over 243 EndFraction S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction S 5 = StartFraction two-thirds (1 minus (one-third) Superscript 5 Baseline) Over (1 minus one-third) EndFraction S = StartFraction one-third Over (1 minus two-thirds) EndFraction S = StartFraction two-thirds Over (1 minus one-third) EndFraction
Mathematics
2 answers:
Troyanec [42]3 years ago
5 0

Answer:

A

Step-by-step explanation:

edge 2020

kondaur [170]3 years ago
4 0

Answer:

S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction

Step-by-step explanation:

Given the geometric series:

1/3+2/9+4/27+8/81+16/243

First we must know that the series is a finite series with just 5terms.

Before we can know the formula to calculate sum of the first five terms of the series, we must determine its common ratio (r) first.

r = (2/9)÷1/3 = 4/27÷2/9= 8/81÷4/27

r = 2/9 × 3/1

r = 2/3

Similarly;

r = 4/27×9/2

r = 2/3

Since all values of r is the as them the common ratio is 2/3.

If r< 1 in geometric series, then the formula for finding its sum is applicable

Sn = a(1-rⁿ)/1-r

a is the first term = 1/3

r is the common ratio = 2/3

n is the number of terms = 5

Substituting the values in the formula we have:

S5 = 1/3{1-(2/3)^5}/1-2/3

This gives the requires equation

S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction

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