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Find a Formula for the Sum ∑k=1n(k2−2k+3)\sum _ { k = 1 } ^ { n } \left( k ^ { 2 } - 2 k + 3 \right)

Question 23

Essay

Find a formula for the sum ∑k=1n(k2−2k+3)\sum _ { k = 1 } ^ { n } \left( k ^ { 2 } - 2 k + 3 \right) and then use it to calculate the sum for n = 100, n = 500, and n = 1000.

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