Problem 87 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the sum. $$\sum_{i=1}^{5}(2 i+1)$$

Step-by-Step Solution

Answer

The sum of the series from i=1 to i=5 for the function \(2i+1\) is 35.

Step 1: Calculate the term for i=1

Substitute i=1 into equation \(2i+1\). This equals \(2*1+1 = 3\)

Step 2: Calculate the term for i=2

Substitute i=2 into equation \(2i+1\). This equals \(2*2+1 = 5\)

Step 3: Calculate the term for i=3

Substitute i=3 into equation \(2i+1\). This equals \(2*3+1 = 7\)

Step 4: Calculate the term for i=4

Substitute i=4 into equation \(2i+1\). This equals \(2*4+1 = 9\)

Step 5: Calculate the term for i=5

Substitute i=5 into equation \(2i+1\). This equals \(2*5+1 = 11\)

Step 6: Add the calculated results

Add together all the calculated results from i=1 to i=5. This equals \(3+5+7+9+11 = 35\)