Câu hỏi của Hải Tiền Hoàng

Question

tìm n thuộc N biết (1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062

𝙳𝚁𝚂_𝙷𝙴𝙻𝚃𝚁𝙸𝚇 · Accepted Answer

(1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062= ( $\dfrac{6}{2.3}$ -$\dfrac{2}{2.3}$ ). ($\dfrac{12}{3.4}$ - $\dfrac{2}{3.4}$ )......( $\dfrac{9900}{99.100}$ - $\dfrac{2}{99.100}$ )= 4/2.3 .10/3.4..... 9898/99.100= 1.4/2.3 . 2.5/3.4 ....  98.101/99.100=$\dfrac{1.2.3.4...98}{2.3...99}$ . $\dfrac{4.5.6...101}{3.4.5...100}$ = 1/99.101/3= 101/297Câu trả lời: (1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062= ( $\dfrac{6}{2.3}$ -$\dfrac{2}{2.3}$ ). ($\dfrac{12}{3.4}$ - $\dfrac{2}{3.4}$ )......( $\dfrac{9900}{99.100}$ - $\dfrac{2}{99.100}$ )= 4/2.3 .10/3.4..... 9898/99.100= 1.4/2.3 . 2.5/3.4 ....  98.101/99.100=$\dfrac{1.2.3.4...98}{2.3...99}$ . $\dfrac{4.5.6...101}{3.4.5...100}$ = 1/99.101/3= 101/297

hoàng · Answer

(1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062

= ( $\dfrac{6}{2.3}$ -$\dfrac{2}{2.3}$ ). ($\dfrac{12}{3.4}$ - $\dfrac{2}{3.4}$ )......( $\dfrac{9900}{99.100}$ - $\dfrac{2}{99.100}$ )

= 4/2.3 .10/3.4..... 9898/99.100

= 1.4/2.3 . 2.5/3.4 .... 98.101/99.100

=$\dfrac{1.2.3.4...98}{2.3...99}$ . $\dfrac{4.5.6...101}{3.4.5...100}$

= 1/99.101/3

= 101/297

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