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posted by  StrickerXY on 10/3/2008 12:28:23 PM  |  status: Live  

induction

Course Textbook Chapter Problem
Discrete Math Discrete mathematics and its applications, sixth edition, kenneth rosen N/A N/A
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Use induction to prove the following:

11 − 6 is divisible by 5, for all n ³ 1.
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posted by velixy on 10/3/2008 2:39:21 PM  |  status: Live
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Response Details:
 

Use induction to prove the following:

 p(n) := (11.n − 6.n)  is divisible by 5, for all n ³ 1.
 
 p(n) := (11.n − 6.n)  ==> n=1 =>  p(1) = 11-6 = 5   is divisible by 5
 
 
LET   p(k) := (11.k − 6.k) = 5.k    true   is divisible by 5
 
we have to show
 p(k+1) := (11.(k+1) − 6.(k+1)) is divisible by 5
 
 p(k+1) := (11.k+11 − 6.k-6) = 11k -6k  + 11-6=  5k + 5  = 5( k+1) is divisible by 5
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