\(=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(=\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{15.16}\)

\(=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

=\(\frac{1}{8}\)

Tích cho mình nhé cảm ơn 

\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(=2\left(\frac{4}{16}-\frac{1}{16}\right)\)

\(=2\times\frac{3}{16}\)

\(=\frac{6}{16}=\frac{3}{8}\)

Complete the following sentences with superlatives.

1. My dad is (fun)_____the funniest______man in the world

2. Whales are (heavy)_____the heaviest_________animals in the world

3. Pandas are (cute)_______the cutest_________animals in the world

4. My bedroom is (comfortable)_____the most comfortable___________room in my house

5. I am (bad)________the worst__________cook in the world

6. For English people, Japanese is (difficult)____difficult_____language to learn

7. That was (sad)_____the sadest_____film I've ever seen

8. My sister is(tidy)______the tidiest________person I have ever known

9. My grandmother is(old)_________the oldest_______person in my family

10. That was(strange)_____the strangest_____________book I've ever read

11.(far)_______the farthest________I've ever travelled is from London to San Francisco

12. What's(dangerous)____the most dangerous_________animal in your country?

13. Spain is(sunny)______the sunniest_______country in Europe

14. What's(hot)______the hottest_______place you've ever visited?

15. What's(late)________the latest_____you've ever stayed up at night?

1.funs
2.heavys
3.cutes
4cmfortables
5.

Ta có: \(\frac{1}{2^2}>\frac{1}{2.3}\)

           \(\frac{1}{3^2}>\frac{1}{3.4}\)

            .... .... ..........

            \(\frac{1}{10^2}>\frac{1}{10.11}\)

\(\Rightarrow S>\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\)

\(\Rightarrow S>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)

\(\Rightarrow S>\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\left(đpcm\right)\)

Cảm ơn

\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}\)

\(\Leftrightarrow S>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)

\(\Leftrightarrow S>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

\(\Leftrightarrow S>\frac{1}{2}-\frac{1}{11}\)

\(\Leftrightarrow S>\frac{11}{22}-\frac{2}{22}\)

\(\Leftrightarrow S>\frac{9}{22}\left(đpcm\right)\)

\(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)

=> \(3\left(3x-\frac{1}{2}\right)^3=-\frac{1}{9}\)

=> \(\left(3x-\frac{1}{2}\right)^3=-\frac{1}{9}:3\)

=> \(\left(3x-\frac{1}{2}\right)^3=-\frac{1}{27}\)

=> \(\left(3x-\frac{1}{2}\right)^3=\left(-\frac{1}{3}\right)^3\)

=> \(3x-\frac{1}{2}=-\frac{1}{3}\)

=> \(3x=-\frac{1}{3}+\frac{1}{2}\)

=> \(3x=\frac{1}{6}\)

=> x = 1/6 : 3

=> x = 1/18

\(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)

\(3.\left(3x-\frac{1}{2}\right)^3=\frac{-1}{9}\)

\(\left(3x-\frac{1}{2}\right)^3=\frac{-1}{27}=\left(\frac{-1}{3}\right)^3\)

\(3x-\frac{1}{2}=\frac{1}{3}\)

\(3x=\frac{5}{6}\)

\(x=\frac{5}{18}\)

Vậy...

Đề bài?

Đúng jui đó bn Hạ Ninh !!!

 bằng 2

1+1=2

hok tốt

phương anh###

Ta có: \(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)

= \(15.\left(\frac{1}{90.94}+\frac{1}{94.98}+\frac{1}{98.102}+...+\frac{1}{146+150}\right)\)

= \(15.\left[\frac{1}{4}.\left(\frac{4}{90.94}+\frac{4}{94.98}+\frac{4}{98.102}+...+\frac{4}{146+150}\right)\right]\)

= \(15.\left[\frac{1}{4}.\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\right]\)

= \(15.\left[\frac{1}{4}.\left(\frac{1}{90}-\frac{1}{150}\right)\right]\)

= \(15.\left(\frac{1}{4}.\frac{1}{225}\right)\)

= \(=\frac{1}{60}\)

Bài làm

   \(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)

= \(15.\frac{1}{90.94}+15.\frac{1}{94.98}+15.\frac{1}{98.102}+...+15.\frac{1}{146.150}\)

= \(15.\left(\frac{1}{90.94}+\frac{1}{94.98}+\frac{1}{98.102}+...+\frac{1}{146.150}\right)\)

= \(15.\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\)

= \(15.\left(\frac{1}{90}-\frac{1}{150}\right)\)

= \(15.\left(\frac{5}{450}-\frac{3}{450}\right)\)

= \(15.\frac{2}{450}\)

= \(\frac{2}{30}\)

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