Mình làm bài cuối nhé bạn:v
\(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};\dfrac{1}{4^2}< \dfrac{1}{3.4}+...+\dfrac{1}{100^2}< \dfrac{1}{99.100}\)
\(\Rightarrow2+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< 2+\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}=2+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=3-\dfrac{1}{100}< 3\)
=> Đpcm
Giúp mình với, mình rảnh vcl được chơi đến 4h sáng
Bài 1:
a) \(\dfrac{2}{3}+\dfrac{-5}{8}=\dfrac{16}{24}+\dfrac{-15}{24}=\dfrac{1}{24}\)
b) \(\dfrac{-10}{11}.\dfrac{4}{7}+\dfrac{-10}{11}.\dfrac{3}{7}+1\dfrac{10}{11}\)
\(=\dfrac{-10}{11}.\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{21}{11}\)
\(=\dfrac{-10}{11}.1+\dfrac{21}{11}\)
\(=\dfrac{-10}{11}+\dfrac{21}{11}\)
\(=1\)
c) \(\left(\dfrac{-5}{24}+0,75+\dfrac{7}{12}\right):\left(-2\dfrac{1}{4}\right)\)
\(=\left(\dfrac{-5}{24}+\dfrac{3}{4}+\dfrac{7}{12}\right):\dfrac{-9}{4}\)
\(=\dfrac{9}{8}:\dfrac{-9}{4}\)
\(=\dfrac{-1}{2}\)
Bài 2:
a) \(x-\dfrac{1}{3}=\dfrac{5}{4}\)
\(x=\dfrac{5}{4}+\dfrac{1}{3}\)
\(x=\dfrac{19}{12}\)
b) \(\dfrac{2}{3}x-\dfrac{4}{9}=\dfrac{2}{9}\)
\(\dfrac{2}{3}x=\dfrac{2}{9}+\dfrac{4}{9}\)
\(\dfrac{2}{3}x=\dfrac{2}{3}\)
\(x=\dfrac{2}{3}:\dfrac{2}{3}\)
\(x=1\)
c) \(\left|2x+\dfrac{2}{7}\right|=\dfrac{1}{2}\)
\(\Rightarrow2x+\dfrac{2}{7}=\dfrac{1}{2}\) hoặc \(2x+\dfrac{2}{7}=\dfrac{-1}{2}\)
\(x=\dfrac{3}{28}\) hoặc \(x=\dfrac{-11}{28}\)
Bài 3:
Giải
a) Số h/s thích bóng đá là:
400.25%=100 (h/s)
Số h/s thích cầu lông là:
100.\(\dfrac{4}{5}\) =80 (h/s)
Số h/s thích bóng rổ là:
400-(100+80)=220 (h/s)
b) Số h/s tăng năm nay so với năm ngoái là:
220.10%=22 (h/s)
Năm ngoái có số h/s thích bóng rổ là:
220-22=198 (h/s)
Bài 5:
\(A=2+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}\)
Ta thấy:
\(\dfrac{1}{2^2}=\dfrac{1}{2.2}< \dfrac{1}{1.2}\)
\(\dfrac{1}{3^2}=\dfrac{1}{3.3}< \dfrac{1}{2.3}\)
\(\dfrac{1}{4^2}=\dfrac{1}{4.4}< \dfrac{1}{3.4}\)
\(...\)
\(\dfrac{1}{100^2}=\dfrac{1}{100.100}< \dfrac{1}{99.100}\)
\(\Rightarrow A< 2+\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(\Rightarrow A< 2+\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(\Rightarrow A< 2+1-\dfrac{1}{100}\)
\(\Rightarrow A< 3-\dfrac{1}{100}\)
\(\Rightarrow A< 3\left(đpcm\right)\)
Chúc bạn học tốt!
