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8.4_bzca5e

# 8.4_bzca5e - 1 3 n n n n-=(a(b(c(d 2 Find S for the series...

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Section 8.4 Mathematical Induction

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The Principle of Mathematical Induction

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Visualizing Summation Formulas
Example 1, 1. 2 2 2 2 2 For the given statement S , write the three statements S , (2 1)(2 1) : 1 3 5 7 ... (2 1) 3 n k K n S S n n n S n + - + + + + + + - =

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Proving Statements about Positive Integers Using Mathematical Induction

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Step 1
Step 2

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Example Use mathematical induction to prove that 5 ( 1) 5 10 15 20 ... 5 2 n n n + + + + + + =
Example 2 3 1 Use mathematical induction to prove that 4 1 1 4 4 4 . . .4 3 n n - - + + + + =

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Example 2 2 2 2 2 Use mathematical induction to prove that (2 1)(2 1) 1 3 5 7 ... (2

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Unformatted text preview: 1) 3 n n n n-+ + + + + +-= (a) (b) (c) (d) 2 Find S for the series 1+3+5+7+. . .+(2n-1)=n k 2 2 2 2 1 3 5 . . 1 3 5 . . 1 3 5 . . 1 3 5 . . .+(k+2)=(k+2) .+(2k+1)=(k+1) .+(2k-1)=k .+(2k+1)=k + + + + + + + + + + + + (a) (b) (c) (d) 2 1 Find S for the series 1+3+5+7+. . .+(2n-1)=n K + 2 2 1 3 5 . . 1 3 5 . . 2k 2k+1 1 3 5 . . .+(2k+1)=(k+1) .+(2k+1)= .+(2k-1)=k(k+1) 1 + 3 + 5 +. . . +(2k-1)=3k(k+1) + + + + + + + + + +...
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8.4_bzca5e - 1 3 n n n n-=(a(b(c(d 2 Find S for the series...

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