Question 117

What is the sum of integers 54 through 196 inclusive?

Solution

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Sum of integers from 54 to 196 = (sum of integers from 1 to 196) - (sum of integers from 1 to 53) 

Sum of first N natural numbers = (N)(N+1)/2

Sum from 1 to 196 = (196)(197)/2 = 98 × 197 = 19306

Sum from 1 to 53 = (53)(54)/2 = 53 × 27 = 1431

Sum of integers from 54 to 196 = 19306 - 1431 = 17875 

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