`1^4/(1cdot3)+2^4/(3cdot5)+...+n^4/((2n-1)(2n+1))=(n(n+1)*(n^2+n+1))/(6(2n+1))` prove using mathematical induction

Expert Answers

An illustration of the letter 'A' in a speech bubbles

First you need to check if the equality holds for `n=1.` ` `



Now we assume that equality holds for all numbers less or equal to `n.`

And now we make inductive step in which we prove that equality holds for `n+1` as well.


By our assumption this equals to


`((1 + n) (6 + 9 n + 5 n^2 + n^3))/(6 (3 + 2 n))=`



This means that our equality holds for `n+1` which completes inductive step meaning we have proven the equality by mathematical induction.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial