Question

1. find the first three partial sums of the series.

2 + 19 + 54 + 113 + 202 + 327 + ...

1. write your answers as integers or fractions in simplest form.

s₁ =
s₂ =
s₃ =

Explanation:

Step1: Find \( S_1 \)

The first partial sum \( S_1 \) is just the first term of the series. The first term is 2, so \( S_1 = 2 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first term is 2 and the second term is 19. So \( S_2 = 2 + 19 = 21 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first term is 2, the second is 19, and the third is 54. So \( S_3 = 2 + 19 + 54 = 75 \).

Answer:

\( S_1 = 2 \)
\( S_2 = 21 \)
\( S_3 = 75 \)