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Help with Induction Questions (1 Viewer)

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1) Prove, for all positive integers , the identity


2) The sequence is given by and for

a) Prove by induction that for , , where

b) Hence find the limiting value of as

3) A sequence is defined by where and is a positive integer.

a) Use induction to show that (the 2^n-1 is the power of the adjacent of fraction)

b) Hence find the limiting value of as becomes large.

Any help would greatly be appreciated!
 

Drongoski

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1) Prove, for all positive integers , the identity


2) The sequence is given by and for

a) Prove by induction that for , , where

b) Hence find the limiting value of as

3) A sequence is defined by where and is a positive integer.

a) Use induction to show that (the 2^n-1 is the power of the adjacent of fraction)

b) Hence find the limiting value of as becomes large.

Any help would greatly be appreciated!
Q2


Very heavy LaTeX typing! I'll skip the many little steps that you can easily do yourself.

a) OK - you can show true for n=1.

Let formula hold for n = k >=1





.: if true for n = k, true also for n = k+1

So you have essentially proven the formula.

b)



I will only do this bit. Hope it helps.
 
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