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Find a Formula for the Sum ∑k=1n(k2+2k+2)n3\sum _ { k = 1 } ^ { n } \frac { \left( k ^ { 2 } + 2 k + 2 \right) } { n ^ { 3 } }

Question 27

Essay

Find a formula for the sum ∑k=1n(k2+2k+2)n3\sum _ { k = 1 } ^ { n } \frac { \left( k ^ { 2 } + 2 k + 2 \right) } { n ^ { 3 } } and then use it to calculate the sum for n = 100, n = 500, and n = 1000.

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