Evaluate the Summation sum from i=1 to 15 of -i-6

Problem

(∑_i=1^15)(−i−6)

Solution

1. Split the summation into two separate parts using the linearity property of sums.

(∑_i=1^15)(−i−6)=−(∑_i=1^15)(i)−(∑_i=1^15)(6)

2. Apply the arithmetic series formula for the first part, where (∑_i=1^n)(i)=(n*(n+1))/2

(∑_i=1^15)(i)=(15*(15+1))/2

(∑_i=1^15)(i)=(15⋅16)/2

(∑_i=1^15)(i)=120

3. Apply the constant sum formula for the second part, where (∑_i=1^n)(c)=n*c

(∑_i=1^15)(6)=15⋅6

(∑_i=1^15)(6)=90

4. Combine the results to find the final value.

−120−90=−210

Final Answer

(∑_i=1^15)(−i−6)=−210

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