Question

find the first three partial sums of the series.
8 + 32 + 128 + 512 + 2048 + 8192 + …
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 8, so \( S_1 = 8 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. So we add the first term (8) and the second term (32): \( S_2 = 8 + 32 = 40 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. We add the first term (8), the second term (32), and the third term (128): \( S_3 = 8 + 32 + 128 = 168 \).

Answer:

\( S_1 = 8 \)
\( S_2 = 40 \)
\( S_3 = 168 \)