Question

How do you evaluate the sum represented by `sum_(k=50)^300k^3`?

Answer 1

The question is unclear, but if you meant `sum_(n=1)^300 k^3` with `k = "(constant) " 50`,
then
`sum_(n=1)^300 k^3 = 300*(50)^3 = 37500000`

Explanation:

If `k=50` then `k^3 = 125000` (a constant)

`sum_(n=1)^p c` for any constant `c`
`color(white)("XXXX")= p*c`

Answer 2

Explanation:

This is the question. i don't understand this.

You can read this "the sum, from k equals 50 to 300, of k to the third"

or "the sum, of k to the third", from k equals 50 to 300"

There are other ways to say it as well, but these two are enough to start.

(for example you could say "from k = 50 to k= 300"

Answer 3

Use formula for `sum_(k=1)^n k^3` to find `sum_(k=50)^300 k^3 = 2037021875`

Explanation:

Use `sum_(k=1)^n k^3 = (n^2+n)^2/4` (proved in another question recently).

See: http://socratic.org/questions/how-do-you-evaluate-the-sum-represented-by-with-n-3-any-examples

Then:

`sum_(k=50)^300 k^3 = sum_(k=1)^300 k^3 - sum_(k=1)^49 k^3`

`=(300^2+300)^2/4 - (49^2+49)^2/4`

`=90300^2/4 - 2450^2/4`

`=45150^2-1225^2`

`=2038522500-1500625`

`=2037021875`