\(\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+...+\frac{5^2}{96\cdot101}\)

\(=5\left(\frac{5^{}}{1\cdot6}+\frac{5^{}}{6\cdot11}+\frac{5^{}}{11\cdot16}+...+\frac{5^{}}{96\cdot101}\right)\)

\(=5\left(1-\frac16+\frac16-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\cdots+\frac{1}{96}-\frac{1}{101}\right)\)

\(=5\left(1-\frac{1}{101}\right)\)

\(=5\cdot\frac{100}{101}\)

\(=\frac{500}{101}\)

Ta có:

+) \(\begin{cases}\frac{1}{201}<\frac{1}{200}\\ \frac{1}{202}<\frac{1}{200}\\ \ldots\\ \frac{1}{250}<\frac{1}{200}\end{cases}\)

\(\rArr\frac{1}{201}+\frac{1}{202}+\cdots+\frac{1}{250}<\frac{1}{200}+\frac{1}{200}+\cdots+\frac{1}{200}=\frac{50}{200}=\frac14\) (1)

+) \(\begin{cases}\frac{1}{251}<\frac{1}{250}\\ \frac{1}{252}<\frac{1}{250}\\ \ldots\\ \frac{1}{300}<\frac{1}{250}\end{cases}\)

\(\rArr\frac{1}{251}+\frac{1}{252}+\cdots+\frac{1}{300}<\frac{1}{250}+\frac{1}{250}+\cdots+\frac{1}{250}=\frac{50}{250}=\frac15\) (2)

Từ (1) và (2) suy ra:

\(A=\frac{1}{201}+\frac{1}{202}+\frac{1}{203}+\cdots+\frac{1}{300}<\frac14+\frac15=\frac{9}{20}\)

Vậy \(A<\frac{9}{20}\)

\(12+x:5=15\times2\)

\(12+x:5=30\)

\(x:5=30-12\)

\(x:5=18\)

\(x=18\times5\)

\(x=90\)

a) \(\frac{10}{24}+\frac{1}{12}\)

\(=\frac{5\times2}{12\times2}+\frac{1}{12}\)

\(=\frac{5}{12}+\frac{1}{12}\)

\(=\frac{6}{12}\)

\(=\frac12\)

b) \(\frac{15}{18}-\frac16\)

\(=\frac{5\times3}{6\times3}-\frac16\)

\(=\frac56-\frac16\)

\(=\frac46\)

\(=\frac23\)

c) \(\frac37-\frac{6}{21}\)

\(=\frac37-\frac{2\times3}{7\times3}\)

\(=\frac37-\frac27\)

\(=\frac17\)

d) \(\frac23+\frac{5}{15}\)

\(=\frac23+\frac{1\times5}{3\times5}\)

\(=\frac23+\frac13\)

\(=\frac33\)

\(=1\)

\(x\left(\frac12+\frac23\right)=\frac73+\frac32\)

\(\frac76x=\frac{23}{6}\)

\(x=\frac{23}{6}:\frac76\)

\(x=\frac{23}{6}\cdot\frac67\)

\(x=\frac{23}{7}\)

Vậy \(x=\frac{23}{7}\)

\(4\frac{3}{100}=\frac{403}{100}=4,03\)
→ Chọn B

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Tham khảo bài viết của mình:

I want to live in a house far away in the future. It is far from the city, the streets, and all the noisy places. I want my house to be in a peaceful and quiet neighborhood. I will surround my house with flowers and trees. I will have the most beautiful garden anyone has ever seen. My pets will have a lot of space to play and run around. I don't have any pet now, but I will get one when I have my own house. Plus, I love doing things by myself, so I won't have many devices in my house.

\(\frac{11}{4}\times\frac{8}{14}\times\frac{7}{11}\times\frac35\)

\(=\frac{11\times8\times7\times3}{4\times14\times11\times5}\)

\(=\frac{11\times2\times4\times7\times3}{4\times2\times7\times11\times5}\)

\(=\frac35\)

\(\frac{27}{45}+\frac{12}{30}\)

\(= \frac{3 \times 9}{5 \times 9} + \frac{2 \times 6}{5 \times 6}\)

\(= \frac{3}{5} + \frac{2}{5}\)

\(= \frac{3 + 2}{5}\)

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

\(= 1\)