ExplanationStart by determining the first few terms to see if there is a pattern, as there often is in sequence questions:

1st term: n = 1 \(1 + (-1)^n\) → \(1 + (-1)^1\) → 1 + –1 → 0

2nd term: n = 2 \(1 + (-1)^n\) → \(1 + (-1)^2\) → 1 + 1 → 2

3rd term: n = 3 \(1 + (-1)^n\) → \(1 + (-1)^3\) → 1 + –1 → 0

4th term: n = 4 \(1 + (-1)^n\) → \(1 + (-1)^4\) → 1 + 1 → 2

As you can see, all odd terms result in 0, while all even terms result in 2. So only the even terms will count in the sum:

1st | 2nd | 3rd | 4th | 5th | 6th | 7th | ... |

0 | 2 | 0 | 2 | 0 | 2 | 0 | ... |

How many even numbers from 1 to 39? 19

Thus the sum = \(19 \times 2 = 38\)

Quantity B is greater.

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Sandy

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