Question

find the first three partial sums of the series.
3 + 4 + 5 + 6 + 7 + 8 + ...
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 3. So, \( S_1 = 3 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. The first two terms are 3 and 4. So, \( S_2 = 3 + 4 = 7 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. The first three terms are 3, 4, and 5. So, \( S_3 = 3 + 4 + 5 = 12 \).

Answer:

\( S_1 = 3 \)
\( S_2 = 7 \)
\( S_3 = 12 \)