proof by induction

Question

1/3+1/15+1/35=...+1/4n²-1=n/2n=1

Answer 1

In proof by induction there are three steps, Basis step, Inductive Hypothesis, Inductive Proof.

 

your premise I believe is P(n): Σ [1 / (4n²-1)] = ?

 

            (but  you wrote this =n/2n=1 which doesn't make sense. Can you correct this part?

 

              Ok thanks Hilton.  )

 

The Basis Step: Prove P(1) which is just 1/3 = 1/3    check

 

Inductive hypothesis step: Assume P(k) true, that is

 

                       1/3 + 1/15 + 1/35 + ... + 1/(4k²+1) = k/(2k+1)

 

Now Prove P(k+1) is true, that is prove

 

                       1/3 + 1/15 + 1/35 + ... + 1/(4k²+1) + 1/[4(k+1)²+1] = (k+1/([2(k+1)+]

 

Can you finish by doing the proper algebra on this last equation. I've given you a big hint by the way I wrote it out.

 

If not comment back and i'll do another step.