Unformatted text preview: Appendix A3
(b) Step 1: The formula holds for n 1, because
1 453 s Appendix A3
(pp. 584592)
1.
a
4 9 k 1 (ak (ak 1 bk)
i k 1 ak bk
k 1 i 1 a1
i b1 . c
1 2 b x
4 7 Step 2: Suppose (ak
k 1 i 1 bk ) k 1 ak bk. Then
k 1 k 1 bk) k 1 i 1 k 1 ak i k 1 i (ak
k 1 i bk) ai
1 (ai bi 1 bi 1)
1 Step 1: x Step 2: bk 1 2 1 2 4 9
c
3 1 x 2 4 9 x
1 2 1 2 1 2 1 2 1 . 18 4 7 1 . 14 ak bk.
k 1 i 1 1 , or 18 The value of 2.
a
2.7591 which assures x
4 is the smaller value, 7
b x The mathematical induction principle now guarantees the original formula for every positive integer n. x (c) Step 1: The formula holds for n 1, because 3.2391 k...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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