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Unformatted text preview: (c) Show how to obtain a better lower bound by splitting the sum into two unequal-sized regions? Just get the high order term right (i.e., do not worry about oors and ceilings and second order terms). How does your bound compare with the lower bound obtained in Part (a)? Problem 3. Consider n s k =1 ( k 2-2 k ) . (a) Use integrals to obtain upper and lower bound bounds. (b) How do your bounds compare with those obtained in Problem 2? (c) How do your bounds compare with the exact polynomial in Problem 1? Problem 4. Find reasonably tight upper and lower bounds for s k =1 k 3 2 k . Justify your answer. You may use a calculator....
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- Fall '11