Question

Write the geometric series in expanded form: Σ(2 * 3^(2i-1), i=1 to 5).

Answer 1

The geometric series Σ(2 * 32i-1, i=1 to 5) in expanded form is 2 * 3 + 2 * 27 + 2 * 243 + 2 * 2187 + 2 * 19683.

Step-by-step explanation:

The question asks to write the geometric series expansion of Σ(2 * 32i-1, i=1 to 5) in expanded form. To expand the series, we will calculate each term separately for i=1 to 5.

For i=1: 2 * 32*1-1 = 2 * 31 = 2 * 3

For i=2: 2 * 32*2-1 = 2 * 33 = 2 * 27

For i=3: 2 * 32*3-1 = 2 * 35 = 2 * 243

For i=4: 2 * 32*4-1 = 2 * 37 = 2 * 2187

For i=5: 2 * 32*5-1 = 2 * 39 = 2 * 19683

Thus, the expanded form of the series is 2 * 3 + 2 * 27 + 2 * 243 + 2 * 2187 + 2 * 19683.

Answer 2

The geometric series Σ(2 * 3^(2i-1), i=1 to 5) can be expanded as 6 + 18 + 54 + 162 + 486.

Step-by-step explanation:

The geometric series Σ(2 * 3^(2i-1), i=1 to 5) can be expanded as follows:

First term: 2 * 3^(2(1)-1) = 2 * 3 = 6

Second term: 2 * 3^(2(2)-1) = 2 * 9 = 18

Third term: 2 * 3^(2(3)-1) = 2 * 27 = 54

Fourth term: 2 * 3^(2(4)-1) = 2 * 81 = 162

Fifth term: 2 * 3^(2(5)-1) = 2 * 243 = 486

Therefore, the expanded form of the geometric series is 6 + 18 + 54 + 162 + 486.