Question

find the first four partial sums of the series.
27 - 27 + 27 - 27 + 27 - 27 + …
write your answers as integers or fractions in simplest form.
s₁ =
s₂ =
s₃ =
s₄ =

Explanation:

Step1: Find \( S_1 \)

The first partial sum \( S_1 \) is the first term of the series. The series starts with 27, so \( S_1 = 27 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first two terms are 27 and -27. So \( S_2 = 27 + (-27) = 0 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first three terms are 27, -27, and 27. So \( S_3 = 27 + (-27) + 27 = 27 \).

Step4: Find \( S_4 \)

The fourth partial sum \( S_4 \) is the sum of the first four terms. The first four terms are 27, -27, 27, and -27. So \( S_4 = 27 + (-27) + 27 + (-27) = 0 \).

Answer:

\( S_1 = 27 \)
\( S_2 = 0 \)
\( S_3 = 27 \)
\( S_4 = 0 \)