Question

Giá trị biểu thức:

A=\(\frac{1}{19}\)+\(\frac{9}{19.29}\)+\(\frac{9}{19.29}\)+......+\(\frac{9}{1999.2009}\)

Answer 1

Ta có:

A=\(\frac{1}{19}\)+\(\frac{9}{19\cdot29}\)+\(\frac{9}{29\cdot39}\)+.......+\(\frac{9}{1999\cdot2009}\)

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{10}{19\cdot29}\)+\(\frac{10}{29\cdot39}\)+......+\(\frac{10}{1999\cdot2009}\))

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{1}{19}\)-\(\frac{1}{29}\)+\(\frac{1}{29}\)-\(\frac{1}{39}\)+.....+\(\frac{1}{1999}\)-\(\frac{1}{2009}\))

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{1}{19}\)-\(\frac{1}{2009}\))

A=\(\frac{200}{2009}\)

Vậy A=\(\frac{200}{2009}\)

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Answer 2

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Answer 3

là 200/2009 mình làm rồi