Calculate Cubes: Calculate the cubes of each number from 1 to 20 and alternate the signs starting with positive for 13.$13=1, 23=8, 33=27, ..., 193=6859, 203=8000).
Sum Series with Signs: Sum the series with alternating signs: 1−8+27−64+…+6859−8000. The series alternates between adding and subtracting the cubes of consecutive integers.
Use Sum Formula: Use the formula for the sum of cubes of the first n natural numbers: (2n(n+1))2. For odd n, the sum is positive, and for even n, the sum is negative. Sum = (13−23)+(33−43)+…+(193−203).
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