Question

find the first three partial sums of the series.
-1 + 2 + 5 + 8 + 11 + 14 + …
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 \(-1\), so \( S_1=-1 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first term is \(-1\) and the second term is \( 2 \), so \( S_2=-1 + 2=1 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first term is \(-1\), the second term is \( 2 \), and the third term is \( 5 \), so \( S_3=-1 + 2+5 = 6 \).

Answer:

\( S_1=-1 \)
\( S_2 = 1 \)
\( S_3=6 \)