Question

Use the properties of summation and Theorem to evaluate the sum. use the summation capabilities of a graphing utility to verify your result.

Answer 1

Step 1:

The expression is .

Using summation formula .

Here, and .

.

.

Step 2:

Graph the summation expression .

Observe the graph, the summation value of is .

Solution:

.

Answer 2

Step 1:

The expression is .

Using summation formula .

Here, and .

.

.

Step 2:

Graph the summation expression .

Observe the graph, the summation value of is .

Solution:

.