Use Gauss's approach to find the following sums (do not use formulas).
a. 1 + 2 + 3 + 4 +...+ 102
b. 1 + 3 + 5 + 7 +...+1001
a. The sum of the sequence is ?
My answer 102-51(103)= 5,253
b. The sum of the sequence is?
My answer 500.3(1,002)=501,300.6
Are my answers correct? If not why, and how do I get the correct answers?
1 answer
Yes, your answers are correct. Gauss's approach involves adding the first and last numbers in the sequence and then multiplying the result by the number of terms in the sequence. For the first sequence, the first number is 1 and the last number is 102, so the sum is (1 + 102) x (102/2) = 5,253. For the second sequence, the first number is 1 and the last number is 1001, so the sum is (1 + 1001) x (501/2) = 501,300.6.
1 answer