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Unformatted text preview: 1 5 ( n + 1 ) 5 + 1 2 ( n + 1 ) 4 + 1 3 ( n + 1 ) 3 1 30 ( n + 1 ). 1.8 Find a formula for 1 + 3 + 5 ++ ( 2 n 1 ) , and use mathematical induction to prove that your formula is correct. Solution. We prove by induction on n 1 that the sum is n 2 . Base Step . When n = 1, we interpret the left side to mean 1. Of course, 1 2 = 1, and so the base step is true. Inductive Step . 1 + 3 + 5 + + ( 2 n 1 ) + ( 2 n + 1 ) = 1 + 3 + 5 + + ( 2 n 1 ) ] + ( 2 n + 1 ) = n 2 + 2 n + 1 = ( n + 1 ) 2 ....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
 Fall '11
 KeithCornell

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