Write the following in sigma notation $$ 1+8+27+64+125 $$

Question

UpStudy AI · Accepted Answer

The given series is:

$$ 1 + 8 + 27 + 64 + 125 $$

Let's analyze the pattern:

- $$1 = 1^3$$
- $$8 = 2^3$$
- $$27 = 3^3$$
- $$64 = 4^3$$
- $$125 = 5^3$$

Each term is the cube of its position in the sequence. Therefore, the series can be expressed using sigma (summation) notation as follows:

$$
\sum_{k=1}^{5} k^3
$$

This summation means that you sum the cubes of $$k$$ starting from $$k = 1$$ up to $$k = 5$$.

**Final Answer:**
$$
\sum_{k=1}^{5} k^{3}
$$
$$ \sum_{k=1}^{5} k^{3} $$

Write the following in sigma notation \( 1+8+27+64+125 \)