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Problem 44: (Induction With Sum Of Odds)

Notice that $$ \begin{align} 1&=1 \\ 1+3&=4 \\ 1+3+5&=9 \\ 1+3+5+7&=16 \\ 1+3+5+7+9&=25. \end{align} $$ Make a conjecture about the sum of odd numbers by giving a general formula for what you see above. Then prove that your formula is valid by using mathematical induction.

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Page last modified on June 11, 2018, at 03:58 PM

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HomePage Schedule Pictures Writing Tips LaTeX Commands External Resources List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Problem Induction With Sum Of Odds Please Login to access more options. Problem 44: (Induction With Sum Of Odds) Notice that $$ \begin{align} 1&=1 \\ 1+3&=4 \\ 1+3+5&=9 \\ 1+3+5+7&=16 \\ 1+3+5+7+9&=25. \end{align} $$ Make a conjecture about the sum of odd numbers by giving a general formula for what you see above. Then prove that your formula is valid by using mathematical induction. The following pages link to this page. Problem.InductionWithSumOfOdds Schedule.20180530 Schedule.20180601 Schedule.20180604 Schedule.AllProblems Here are the old pages. Edit Page History Source Attach File Backlinks List Group Page last modified on June 11, 2018, at 03:58 PM
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