Unformatted text preview: 2 , or, in general , 1+3+5+ & & & +2 n ± 1 = n 2 . The base case is when n = 1 , in which case the equation is 1 = 1 2 , which is true. For the induction step, we assume that the equation holds for n = k : 1 + 3 + 5 + & & & + 2 k ± 1 = k 2 Add 2 k + 1 to both sides 1 + 3 + 5 + & & & + (2 k ± 1) + (2 k + 1) = k 2 + 2 k + 1 = ( k + 1) 2 which is the equation when n = k + 1 ....
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 Spring '08
 STAFF
 Mathematical Induction, Natural number

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