Evaluate the Summation sum from k=1 to 6 of 9k

Problem

(∑_k=1^6)(9)*k

Solution

1. Identify the constant factor in the summation. Since 9 is a constant, it can be moved outside the summation symbol.

(∑_k=1^6)(9)*k=9*(∑_k=1^6)(k)

2. Apply the formula for the sum of the first n integers, which is (∑_k=1^n)(k)=(n*(n+1))/2 Here, n=6

(∑_k=1^6)(k)=(6*(6+1))/2

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

(6*(7))/2=42/2

42/2=21

4. Multiply the result of the summation by the constant factor 9 that was moved outside earlier.

9×21=189

Final Answer

(∑_k=1^6)(9)*k=189

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