FMM18: Difference between revisions
From charlesreid1
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There are 1977 terms to add, and surely it would not be a Friday Morning Math Problem if it were so boring as to tediously add so many terms. | |||
You'll also notice the radicals are improper. If we try getting rid of the radicals on the bottom of each term, we get something interesting: | |||
<math> | |||
\dfrac{1}{\sqrt{a} + \sqrt{b}} = \dfrac{(\sqrt{a} - \sqrt{b})}{(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})} | |||
</math> | |||
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Revision as of 02:23, 23 January 2020
Friday Morning Math Problem
Radical Sums
Evaluate the sum:
$ \dfrac{1}{1 + \sqrt{1}} + \dfrac{1}{\sqrt{2} + \sqrt{3}} + \dfrac{1}{\sqrt{3} + \sqrt{4}} + \dots + \dfrac{1}{\sqrt{1977} + \sqrt{1978}} $
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Friday Morning Math Problems weekly math problems
Spider Socks and Shoes FMM1 Sums of Powers of 2 FMM2 Fifty Coins FMM3 The Zeta Monogram FMM4 The Cthulhus Monogram FMM4B Multiplication Logic FMM5 The Termite and the Cube FMM6 Sharing Dump Trucks FMM7 The Flippant Juror FMM8 Bus Routes FMM9 A Robust Bus System FMM9B Square-Free Sequence FMM10 Inferring Rule from Sequence FMM11 Checkerboard Color Schemes FMM12 One-Handed Chords FMM13 First Ace FMM14 Which Color Cab FMM15 Petersburg Paradox Revisited FMM16 A Binomial Challenge FMM17 A Radical Sum FMM18 Memorable Phone Numbers FMM19 Arrange in Order FMM20 A Pair of Dice Games: FMM21
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