EBK SINGLE VARIABLE CALCULUS, VOLUME 1
EBK SINGLE VARIABLE CALCULUS, VOLUME 1
8th Edition
ISBN: 9780100850668
Author: Stewart
Publisher: YUZU
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Chapter E, Problem 39E

Prove formula (e) of Theorem 3 using a method similar to that of Example 5, Solution 1 [start with (1 + i)4i4].

3 Theorem Let c be a constant and n a positive integer. Then

  1. (a) i = 1 n 1 = n
  2. (b) i = 1 n c = n c
  3. (c) i = 1 n i = n ( n + 1 ) 2
  4. (d) i = 1 n i 2 = n ( n + 1 ) ( 2 n + 1 ) 6
  5. (e) i = 1 n i 3 = [ n ( n + 1 ) 2 ] 2
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