Chứng minh 1/4^2+1/6^2+...+1/(2n)^2 < 1/4
Bài 1 Tìm x,y thuộc số nguyên 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Bài 2 Chứng minh A) A= 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B) B= 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Chứng minh 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Bài 4 A = 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sao cho thuộc số nguyên Bài 5 Tính A) 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Trả lời (2)
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ơ
bạn làm thế ai tl đc
bởi _TOM_ 19/12/2018Like (0) Báo cáo sai phạm -
Bài 2:
\(\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{\left(2n\right)^2}< \dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{\left(2n-2\right).2n}\)
\(=\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{\left(2n-2\right).2n}\right).\dfrac{1}{2}\)
\(=\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{12}+...+\dfrac{1}{2n-2}-\dfrac{1}{2n}\right).\dfrac{1}{2}\)
\(=\left(\dfrac{1}{2}-\dfrac{1}{2n}\right).\dfrac{1}{2}\)
\(=\dfrac{1}{4}-\dfrac{1}{2n.2}< \dfrac{1}{4}\)
\(\Rightarrow\dfrac{1}{4^2}+\dfrac{1}{6^2}+\dfrac{1}{8^2}+...+\dfrac{1}{\left(2n\right)^2}< \dfrac{1}{4}\left(đpcm\right)\)
bởi Quyên Trúc 19/12/2018Like (0) Báo cáo sai phạm
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