The expression to find the sum of terms of the series is; Sₙ = 3(1 - ¹/₂ⁿ)
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; https://brainly.com/question/24643676
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