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Muhammad Alfatih

Buku Olimpiade Matematika SD

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Karena $A,B,..,Z$ adalah bilangan asli berurutan dari 3 (dengan kata lain $A=3,B=4,...,Z=28$ ), maka dapat kita simpulkan bahwa $A=B+1,B=C+1,..,Z=Y+1$

 

Perhatikan bahwa $\frac1{AB}=\frac{B-A}{AB}=\frac1A-\frac1B$

 

Maka $\frac1{AB}+\frac1{BC}+\frac1{CD}+..+\frac1{YZ}=\frac1A-\frac1B+\frac1B-\frac1C+\frac1C-\frac1D+..+\frac1Y-\frac1Z=\frac1A-\frac1Z=\frac13-\frac1{28}=\frac{25}{84}$

 

CMIIW

 

 

 

Edited by BeingNotknown Ya
Ada yang ketinggalan :D

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Bisa dilihat A=3,B=4,...,Z=28

Perhatikan bahwa $\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$

Maka, 

1/(A×B)+1/(B×C)+1/(C×D)+........+1/(Y×Z) = $\frac{1}{3x4}+\frac{1}{4x5}+....+\frac{1}{27x28}=1/3-1/4+1/4-1/5+1/5-1/6....+1/27-1/28 = 1/3-1/28 = 25/84$

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On 13/8/2016 at 5:47 PM, Muhammad Alfatih said:

Bagaimana kalo A hingga Z merupakan bilangan prima dimulai dari 2. Gimana cara mengerjakannya

 

Mnurut saya jika prima akan tidak ditemukan polanya

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