Math Is Fun Forum

Hunt

Member

Registered: 2007-09-29

Posts: 9

Limit proof

Consider the expression of q ( a fraction ) as a function of n :

V_2 , V_1 , and D_c are constants. n is a positive integer that varies from 1 till infinity.

It is required to prove that :

I cant think of any possible way to prove that. However , it is clear that q_n tends towards zero . The expression above then makes sense. Any suggestion is appreciated.

Thanks

anons

Guest

Re: Limit proof

How can you sum a constant?

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Limit proof

I didnt include the details of summation of v_1 because it doesnt mattter. We are taking n equal V_1's , meaning the correct expression should be :

So if this helps ,

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Limit proof

Use the fact that if a sequence q_n converges, then limit as n->infinity p(n) = limit as n->infinity p(n+1).  It should just be algebra from there.  Very messy algebra, but algebra none the less.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Limit proof

Thanks Ricky. Before I attempted to do that messy algebra , I tried L.H. rule one more time for the Ln(q_n). I got the right answer. I must have been making some careless mistake somewhere ...