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posted by  Dexter_xp on 8/23/2008 12:56:45 AM  |  status: Closed  

math induction

Course Textbook Chapter Problem
Discrete Math N/A N/A N/A
Question Details:

Use mathematical induction to prove the following is true for every integer, n.
3 + 5 + 7 + . . . + (2 n + 1) = n (n + 2)

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posted by zsm28 on 8/23/2008 3:10:37 AM  |  status: Live
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Dexter_xp's comment:
"thanks a lot!"
Response Details:
if n = 1,
3 = 1*(1 + 2) = 3
so it is true.

Assume it is true for n = k, that is
3 + 5 + 7 + . . . + (2k + 1) = k(k + 2)
For n = k + 1
 3 + 5 + 7 + . . . + (2k + 1) + [2(k + 1) + 1]
= k(k + 2) + [2(k + 1) + 1]
= k2 + 2k + 2k + 3
= k2 + 4k + 3
= (k + 1)(k + 1 + 2)
so it is also true for n = k + 1

By mathematical induction,
3 + 5 + 7 + . . . + (2 n + 1) = n (n + 2)
is true for every integer n.
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