Question

find the first three partial sums of the series.
6 + 7 + 8 + 9 + 10 + 11 + …
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. The first term of the series is 6. So, \( S_1 = 6 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first two terms are 6 and 7. So, \( S_2 = 6 + 7 = 13 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first three terms are 6, 7, and 8. So, \( S_3 = 6 + 7 + 8 = 21 \).

Answer:

\( S_1 = 6 \)
\( S_2 = 13 \)
\( S_3 = 21 \)