Question

Nomor 8 Pakai cara yang benar​

Answer 1

Jawab:

1064

Penjelasan dengan langkah-langkah:

[tex]P=\frac{1}{2\times 3} +\frac{2}{3\times 4} +\frac{3}{4\times 5} ...+\frac{98}{99\times 100}[/tex]

[tex]P=(\frac{1}{2} -\frac{1}{3} )+2(\frac{1}{3} -\frac{1}{4} )+3(\frac{1}{4} -\frac{1}{5} )+...+98(\frac{1}{99} -\frac{1}{100} )[/tex]

[tex]P=\frac{1}{2} +\frac{1}{3} +\frac{1}{4} +...+\frac{1}{99} -\frac{98}{100}[/tex]

[tex]Q=\frac{1}{3\times 5} +\frac{2}{4\times 6} +\frac{3}{5\times 7} +...+\frac{96}{98\times 100}[/tex]

[tex]Q=[\frac{1}{2}( \frac{1}{3} -\frac{1}{5}) +\frac{3}{2} (\frac{1}{5} -\frac{1}{7} )+...+\frac{95}{2} (\frac{1}{97} -\frac{1}{99} )]+[\frac{1}{2\times 3} +\frac{2}{3\times 4} +...+\frac{48}{49\times 50} ][/tex]

[tex]Q=[\frac{1}{6} +\frac{1}{5} +\frac{1}{7} +...+\frac{1}{97} -\frac{95}{2\times 99} ]+[\frac{1}{2} +\frac{1}{3} +...+\frac{1}{49} -\frac{48}{50} ][/tex]

[tex]P-Q[/tex]

[tex]=(\frac{1}{2} +\frac{1}{3} +\frac{1}{4} +...+\frac{1}{99} -\frac{98}{100})-([\frac{1}{6} +\frac{1}{5} +\frac{1}{7} +...+\frac{1}{97} -\frac{95}{2\times 99} ]+[\frac{1}{2} +\frac{1}{3} +...+\frac{1}{49} -\frac{48}{50} ])[/tex]

[tex]= \frac{1}{98} +\frac{1}{99} -\frac{98}{100}-(\frac{1}{6} +\frac{1}{5} +...+\frac{1}{49}-\frac{95}{2\times 99} )-\frac{48}{50}[/tex]

[tex]=(\frac{1}{98} -\frac{14-7}{7\times 14}) +(\frac{1}{99} -\frac{11-9}{9\times 11})+ (-\frac{98}{100} +\frac{48}{50\times 2} -\frac{20-5}{5\times20 }) -(\frac{1}{6} +\frac{1}{6} +\frac{1}{8} +\frac{1}{10} +\frac{1}{12} +\frac{1}{13} +[\frac{1}{15} +\frac{1}{16} +...+\frac{1}{19} ]+[\frac{1}{21}+\frac{1}{22} +...+\frac{1}{49}]-\frac{95}{2\times99 } )[/tex]

dan seterusnya dihitung manual

Sehingga m+n=1064