Evaluate the Summation sum from i=1 to 24 of 4i

Problem

(∑_i=1^24)(4)*i

Solution

1. Factor out the constant 4 from the summation, as it does not depend on the index i

4*(∑_i=1^24)(i)

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

(∑_i=1^n)(i)=(n*(n+1))/2

3. Substitute n=24 into the formula to calculate the sum of the integers from 1 to 24

(∑_i=1^24)(i)=(24*(24+1))/2

4. Simplify the expression by performing the arithmetic.

(24*(25))/2=12⋅25=300

5. Multiply the result of the summation by the constant factor 4 that was factored out in step 1.

4⋅300=1200

Final Answer

(∑_i=1^24)(4)*i=1200

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