Evaluate the Summation sum from i=1 to 8 of 3i

Problem

(∑_i=1^8)(3)*i

Solution

1. Identify the constant factor in the summation. Since 3 is a constant, it can be moved outside the summation symbol.

(∑_i=1^8)(3)*i=3*(∑_i=1^8)(i)

2. Apply the formula for the sum of the first n integers, which is (∑_i=1^n)(i)=(n*(n+1))/2 In this case, n=8

(∑_i=1^8)(i)=(8*(8+1))/2

3. Simplify the expression inside the parentheses and perform the division.

(8*(9))/2=72/2

72/2=36

4. Multiply the result of the summation by the constant factor 3 that was moved outside earlier.

3×36=108

Final Answer

(∑_i=1^8)(3)*i=108

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