Question

Find Y such that :

( 1 / 2 x 4 + 1 / 4 x 6 + 1 / 6 x 8 + ... + 1 / 98 x 100 ) : Y = 147 / 50

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Answer 1

Đặt \(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+....+\frac{1}{98.100}=A\)

<=> \(A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)

<=> \(A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)

<=> \(A=\frac{1}{2}.\frac{49}{100}=\frac{49}{200}\)

lúc đó \(\frac{A}{Y}=\frac{147}{50}\)<=> \(Y=\frac{49}{200}.\frac{50}{147}=\frac{1}{12}\)