Question

find the first five partial sums of the series.
36 + 36 + 36 + 36 + 36 + 36 + ...
write your answers as integers or fractions in simplest form.
s₁ =
s₂ =
s₃ =
s₄ =
s₅ =

Explanation:

Step1: Find \( S_1 \)

The first partial sum \( S_1 \) is just the first term of the series. The series starts with 36, so \( S_1 = 36 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. Each term is 36, so \( S_2 = 36 + 36 = 72 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. So \( S_3 = 36 + 36 + 36 = 108 \).

Step4: Find \( S_4 \)

The fourth partial sum \( S_4 \) is the sum of the first four terms. So \( S_4 = 36 + 36 + 36 + 36 = 144 \).

Step5: Find \( S_5 \)

The fifth partial sum \( S_5 \) is the sum of the first five terms. So \( S_5 = 36 + 36 + 36 + 36 + 36 = 180 \).

Answer:

\( S_1 = 36 \)
\( S_2 = 72 \)
\( S_3 = 108 \)
\( S_4 = 144 \)
\( S_5 = 180 \)