Evaluate the Summation sum from n=0 to 4 of (n^2)/2

Problem

(∑_n=0^4)((n2)/2)

Solution

1. Identify the terms of the summation by substituting each integer value of n from the lower limit 0 to the upper limit 4 into the expression (n2)/2

2. Substitute n=0

0/2=0

3. Substitute n=1

1/2=1/2

4. Substitute n=2

2/2=4/2=2

5. Substitute n=3

3/2=9/2

6. Substitute n=4

4/2=16/2=8

7. Sum the calculated values together:

0+1/2+2+9/2+8

8. Simplify the expression by combining the fractions and the integers:

10/2+10=5+10=15

Final Answer

(∑_n=0^4)((n2)/2)=15

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