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Use the approach in Gauss’s problem to find the following sums of arithmetic sequences (do not use formulas):1+3+5+7+…+1001

Question

Use the approach in Gauss’s problem to find the following sums of arithmetic sequences (do not use formulas):1+3+5+7+…+1001

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Step 1

To find the sum of the given arithmetic sequence using Gauss's approach.

The given sequence is 1+3+5+7+...+1001.

The total number of terms in the sequence is (1+1001)/2 = 1002/2 = 501.

To make the number of terms an even numer,  skip the last term 1001.

Now the sequence become 1+3+5+7+...+999.

Add ith and (n-i)th term of the sequence, where n,i∈[1,500].

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