\(S=\frac{1}{2.2}+\frac{1}{3.3}+......+\frac{1}{9.9}< \frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{8.9}\)

\(\Rightarrow S< 1-\frac{1}{2}+\frac{1}{2}-......+\frac{1}{8}-\frac{1}{9}\)

\(\Rightarrow S< 1-\frac{1}{9}=\frac{8}{9}\)

À quên suýt nữa thì quên mất, nhớ giải chi tiết ra ấy nhé!

\(S=\frac{1}{2.2}+\frac{1}{3.3}+....+\frac{1}{9.9}< \frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{8.9}\)

\(\Rightarrow S< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{8}-\frac{1}{9}\)

\(\Rightarrow S< 1-\frac{1}{9}=\frac{8}{9}\)

1/2.2 + 1/3.3 + 1/4.4 + ... + 1/9.9

> 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/9.10

> 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

> 1/2 - 1/10

> 5/10 - 1/10

> 2/5 (1)

1/2.2 + 1/3.3 + 1/4.4 + ... + 1/9.9

< 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/8.9

< 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9

< 1 - 1/9

< 8/9 (2)

Từ (1) và (2) => 2/5 < 1/2.2 + 1/3.3 + 1/4.4 + ... + 1/9.9 < 8/9

Ta có:\(A=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{10.10}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

Mà \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}< 1\)

=>A<1

\(\text{Ta có: }\frac{1}{2.2}< \frac{1}{1.2};\frac{1}{3.3}< \frac{1}{2.3};.....;\frac{1}{10.10}< \frac{1}{9.10}\)

 \(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{9.10}\)

\(\Rightarrow A< 1-\frac{1}{10}\)

\(\Rightarrow A< \frac{9}{10}< 1\)

A = 1/2.2 + 1/3.3 + 1/4.4 + ... + 1/10.10

A < 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/9.10

A < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10

A < 1 - 1/10 < 1

=> A < 1

S= 1.1! + 2.2! + 3.3! + 4.4! +5.5!

  = 1 + 4 + 18 + 96 + 600

  = 719

bằng 49,5 nhé bạn

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