Question

find the first three partial sums of the series.
22 + 22 + 22 + 22 + 22 + 22 + …
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 the sum of the first term of the series. The first term is 22, so \( S_1 = 22 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first two terms are 22 and 22, so \( S_2 = 22 + 22 = 44 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first three terms are 22, 22, and 22, so \( S_3 = 22 + 22 + 22 = 66 \).

Answer:

\( S_1 = 22 \)
\( S_2 = 44 \)
\( S_3 = 66 \)