Question

find the first three partial sums of the series.
26 - 26 + 26 - 26 + 26 - 26 + ...
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 first term of the series. The series starts with 26, so \( S_1 = 26 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first two terms are 26 and -26. So \( S_2 = 26 + (-26) = 0 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first three terms are 26, -26, and 26. So \( S_3 = 26 + (-26) + 26 = 26 \).

Answer:

\( S_1 = 26 \)
\( S_2 = 0 \)
\( S_3 = 26 \)