Question

Write the geometric series in expanded form e⁵ ³∑ᵢ₌₁ 3(2)ᶦ⁻¹

Answer 1

To write the geometric series in expanded form e⁵ ³∑ᵢ₌₁ 3(2)ᶦ⁻¹, we can use the formula for the sum of a geometric series. The expanded form is 3 + 6 + 12 + 24 + ... + 192.

Step-by-step explanation:

To write the geometric series in expanded form e⁵ ³∑ᵢ₌₁ 3(2)ᶦ⁻¹, we need to first understand the notation being used. The capital sigma (∑) represents summation, and the subscript i=1 indicates that the series starts with i=1. The expression 3(2)ᶦ⁻¹ represents the terms of the series, with i starting at 1 and increasing by 1 in each term.

Using the formula for the sum of a geometric series, we can write the expanded form as:

e⁵ ³∑ᵢ₌₁ 3(2)ᶦ⁻¹ = 3(2)⁰ + 3(2)¹ + 3(2)² + 3(2)³ + ... + 3(2)⁵

Simplifying the exponents, we get:

e⁵ ³∑ᵢ₌₁ 3(2)ᶦ⁻¹ = 3 + 6 + 12 + 24 + ... + 192

So, the expanded form of the geometric series is 3 + 6 + 12 + 24 + ... + 192.