Berapa hasil dari perkalian
[tex]\displaystyle 97\left ( 1-\frac{9}{4^2} \right )\left ( 1-\frac{9}{7^2} \right )\left ( 1-\frac{9}{10^2} \right )\cdots\left ( 1-\frac{9}{97^2} \right )[/tex]
[tex]\displaystyle 97\left ( 1-\frac{9}{4^2} \right )\left ( 1-\frac{9}{7^2} \right )\left ( 1-\frac{9}{10^2} \right )\cdots\left ( 1-\frac{9}{97^2} \right )[/tex]
Jawaban:
[tex]97( 1 - \frac{9}{4 {}^{2} })( 1 - \frac{9}{7 {}^{2} } )(1 - \frac{9}{10 {}^{2} } ) \\ 97 \times \frac{7}{16} (1 - \frac{9}{7 {}^{2} } )(1 - \frac{9}{10 {}^{2} } ) \\ \\ 97 \times \frac{7}{16} \times \frac{40}{49} (1 - ( \frac{9}{10 {}^{2} } = \frac{9}{100})) \\ 97 \times \frac{7}{16} \times \frac{40}{49} \times \frac{91}{100} = \frac{2471560}{78400} \\ factor \: the \: number \: = 2471560 = 1960 \: . \: 1261 \\ factor \: the \: number \: = 78400 = 1960 \: . \: 40 \\ \frac{1960.1261}{1960.40} = \frac{1261}{40} [/tex]
Verified answer
Jawaban:
25
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