Input in W|A this proof by induction problem correctly?

Questions
1

What I want:

AIQSGKZ.png
AIQSGKZ.png601×136 2.24 KB

Current attempt:

prove by induction 1/(n+1) + 1/(n+2) + - Wolfram|Alpha…+%2B+1%2F(2n)+%3E+13%2F24

2

Best so far, but the solution is incorrect…

3

You can use Mathematica:

Sum[1/k, {k, n + 1, 2 n}]

which gives:

-PolyGamma[0, 1 + n] + PolyGamma[0, 1 + 2 n]

which can be evaluated very quickly, leading to n>=2 (n integer).

4

I don’t know hot to use Mathematica… And I was hoping to utilase the step by step solution :slight_smile:

5

Maybe I am missing something. But, if the problem is to show by induction that the inequality is true for n an integer and n >1, then:

  1. Show it is true for n = 2.
  2. Show that if it is true for n-1, it is true for n.
  3. QED

This can be done quite simply, without Mathematica or Alpha.

Best, David

6

Yeah, it’s not that hard, but I wanted to check if my solution is correct.