Pertanyaan

1 + 2 1 + 2 + 3 1 + 3 + 4 1 + ... + 9999 + 10000 1 = ...

$\frac{1}{1 + 2} + \frac{1}{2 + 3} + \frac{1}{3 + 4} + ... + \frac{1}{9999 + 10000} = ...$

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Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

jadi,

$tilde space fraction numerator 1 over denominator 1 plus square root of 2 end fraction equals fraction numerator 1 over denominator 1 plus square root of 2 end fraction space. space fraction numerator 1 minus square root of 2 over denominator 1 minus square root of 2 end fraction equals fraction numerator 1 minus square root of 2 over denominator 1 squared minus open parentheses square root of 2 close parentheses squared end fraction equals fraction numerator 1 minus square root of 2 over denominator negative 1 end fraction equals negative 1 plus square root of 2 tilde space fraction numerator 1 over denominator square root of 2 plus square root of 3 end fraction equals fraction numerator 1 over denominator square root of 2 plus square root of 3 end fraction space. space fraction numerator square root of 2 minus square root of 3 over denominator square root of 2 minus square root of 3 end fraction equals space fraction numerator square root of 2 minus square root of 3 over denominator open parentheses square root of 2 close parentheses squared minus open parentheses square root of 3 close parentheses squared end fraction equals space fraction numerator square root of 2 minus square root of 3 over denominator negative 1 end fraction equals negative square root of 2 plus square root of 3 tilde space fraction numerator 1 over denominator square root of 3 plus square root of 4 end fraction equals fraction numerator 1 over denominator square root of 3 plus square root of 4 end fraction space. space fraction numerator square root of 3 minus square root of 4 over denominator square root of 3 minus square root of 4 end fraction equals space fraction numerator square root of 3 minus square root of 4 over denominator open parentheses square root of 3 close parentheses squared minus open parentheses square root of 4 close parentheses squared end fraction equals fraction numerator square root of 3 minus square root of 4 over denominator negative 1 end fraction equals negative square root of 3 plus square root of 4 tilde space... tilde space fraction numerator 1 over denominator square root of 9999 space plus space square root of 10000 end fraction equals fraction numerator 1 over denominator square root of 9999 space plus space square root of 10000 end fraction space. space fraction numerator square root of 9999 space minus space square root of 10000 over denominator square root of 9999 space minus space square root of 10000 end fraction equals fraction numerator square root of 9999 space minus space square root of 10000 over denominator open parentheses square root of 9999 close parentheses squared space minus space open parentheses square root of 10000 close parentheses squared end fraction equals fraction numerator square root of 9999 space plus space square root of 10000 over denominator negative 1 end fraction equals negative square root of 9999 space plus space square root of 10000$

jadi,

$fraction numerator 1 over denominator 1 plus square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 begin display style plus end style begin display style square root of 3 end style end fraction plus fraction numerator 1 over denominator square root of 3 begin display style plus end style begin display style square root of 4 end style end fraction plus... plus fraction numerator 1 over denominator square root of 9999 begin display style plus end style begin display style square root of 10000 end style end fraction equals open parentheses negative 1 plus square root of 2 close parentheses plus open parentheses negative square root of 2 plus square root of 3 close parentheses plus... plus open parentheses negative square root of 9999 plus square root of 10000 close parentheses equals negative 1 plus square root of 10000 equals negative 1 plus 100 equals 99$