Prove that 1 11 </mfrac> + 1

Jayla Christensen

Jayla Christensen

Answered question

2022-06-08

Prove that 1 11 + 1 12 + + 1 200 1 10 11 + 1 11 12 + + 1 19 20 > 19
My attempt:The denominator is 1 20 using telescopic series.
1 10 11 + 1 11 12 + + 1 19 20 = 1 10 1 11 + 1 11 1 12 + 1 20 = 1 10 1 20 = 1 20
I think we could Prove that the top part of fraction is bigger than 1 but I don't know how.

Answer & Explanation

Hadley Cunningham

Hadley Cunningham

Beginner2022-06-09Added 20 answers

Your calculation for the denominator (telescopic sum and not series) was the hard part, since
1 11 + 1 12 + + 1 200 1 20 > 1 200 + 1 200 + + 1 200 1 20 = 200 10 200 1 20 = 19 20 1 20 = 19

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