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Question: mathematical induction

Question:mathematical induction

Oliver K 1201 Maple
November 12 2008
0

Hi everyone,  to have an example, the following recurrence is given. I want to proof that it converges (and determine the limit for n->infinity).

g:=a(n+1)=3/2+sqrt(1+a(n));

Maple cannot find an explicit  form of a(n), typing rsolve(g,a(n)); gives the input back. One standard approach would be calculating the possible limit by solving the fixed point equation

a=3/2+sqrt(1+a)

this isn't a problem ofc. Further it is necessary to show a(n) is bounded and grows monotonous. So my question is, is Maple a useful tool for mathematical induction ?

Can Maple do the inductive step to show that a(n+1)>a(n) ?

 

Thomas

 

 

 

 

 

 

 

 

 

 
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