Evaluate the Summation sum from n=11 to 30 of n

Problem

(∑_n=11^30)(n)

Solution

1. Identify the summation as an arithmetic series where the first term (a_11)=11 the last term (a_30)=30 and the common difference is 1

2. Calculate the number of terms k in the sequence using the formula k=upper limit−lower limit+1

k=30−11+1

k=20

3. Apply the formula for the sum of an arithmetic series, which is S=k/2*((a_first)+(a_last))

S=20/2*(11+30)

4. Simplify the expression to find the total sum.

S=10*(41)

S=410

Final Answer

(∑_n=11^30)(n)=410

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