Question

Consider the series Three-halves three-fourths StartFraction 3 Over 8 EndFraction StartFraction 3 Over 16 EndFraction ellipsis What expression defines Sn

Answer 1

The expression to find the sum of terms of the series is; Sₙ = 3(1 - ¹/₂ⁿ)

How to solve Geometric series?

We are given the series;

3/2 + 3/4 + 3/8 + 3/16 +.....

Formula for the nth term of a geometric series is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

From our given series;

a = ³/₂

r = (³/₄)/(³/₂) = ¹/₂

We know that Sum of GP when n < 1 is;

Sₙ = a(1 - rⁿ)/(1 - r)

Thus;

Sₙ = ³/₂(1 - ¹/₂ⁿ)/(1 - ¹/₂)

Sₙ = 3(1 - ¹/₂ⁿ)

Thus, the expression to find the sum of terms of the series is; Sₙ = 3(1 - ¹/₂ⁿ)

Read more about Geometric Series at; brainly.com/question/24643676

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