Explanation Definition used: If a m , a m + 1 , ... , a n are real numbers and m and n are integers such that m ≤ n , then ∑ i = m n a i = a m + a m + 1 + a m + 2 + ⋯ + a n − 1 + a n . Theorem used: Let c be a constant and n be a positive integer. Then, ∑ i = 1 n c = n c , ∑ i = 1 n i = n ( n + 1 ) 2 and ∑ i = 1 n i 2 = n ( n + 1 ) ( 2 n + 1 ) 6 . Calculation: By the above definition, the sum ∑ i = 1 n ( i 3 − i − 2 ) expressed as follows. ∑ i = 1 n ( i 3 − i − 2 ) = ∑ i = 1 n i 3 − ∑ i = 1 n i − ∑ i = 1 n 2 = ( n ( n + 1 )

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ISBN: 9781305764583

Author: Stewart

Publisher: CENGAGE C

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Chapter E, Problem 35E

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To find: The value of the sum ∑i=1n(i3−i−2).

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Chapter E, Problem 34E

Chapter E, Problem 36E

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Chapter E Solutions

CALCULUS SINGLE VAR W/ACCESS >CI<

Ch. E - Prob. 1E Ch. E - Prob. 2E Ch. E - Write the sum in expanded form. 3. i=463i Ch. E - Prob. 4E Ch. E - Prob. 5E Ch. E - Write the sum in expanded form. 6. k=58xk Ch. E - Prob. 7E Ch. E - Write the sum in expanded form. 8. j=nn+3j2 Ch. E - Prob. 9E Ch. E - Prob. 10E

Ch. E - Prob. 11E Ch. E - Prob. 12E Ch. E - Prob. 13E Ch. E - Write the sum in sigma notation. 14....Ch. E - Prob. 15E Ch. E - Prob. 16E Ch. E - Prob. 17E Ch. E - Prob. 18E Ch. E - Prob. 19E Ch. E - Prob. 20E Ch. E - Prob. 21E Ch. E - Prob. 22E Ch. E - Prob. 23E Ch. E - Prob. 24E Ch. E - Prob. 25E Ch. E - Prob. 26E Ch. E - Prob. 27E Ch. E - Prob. 28E Ch. E - Prob. 29E Ch. E - Prob. 30E Ch. E - Prob. 31E Ch. E - Prob. 32E Ch. E - Find the value of the sum. 33. i=1n(i+1)(i+2)Ch. E - Prob. 34E Ch. E - Prob. 35E Ch. E - Find the number n such that i=1ni=78.Ch. E - Prob. 37E Ch. E - Prove formula (e) of Theorem 3 using mathematical...Ch. E - Prove formula (e) of Theorem 3 using a method...Ch. E - Prove formula (e) of Theorem 3 using the following...Ch. E - Evaluate each telescoping sum. (a) i=1n[i4(i1)4]...Ch. E - Prove the generalized triangle inequality:...Ch. E - Find the limit. 43. limni=1n1n(in)2 Ch. E - Prob. 44E Ch. E - Prob. 45E Ch. E - Prob. 46E Ch. E - Prob. 47E Ch. E - Prob. 48E Ch. E - Prob. 49E Ch. E - Prob. 50E

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The value of the sum ∑ i = 1 n ( i 3 − i − 2 ) .

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Chapter E Solutions