Question

1.Tìm chữ số tận cùng :

a) 43¹⁷

b) 17⁸

c) (-2015)¹⁷

2. A=1/101+1/102+1/103+...+1/200

Chứng minh A>7/12

 

Answer 1

Ta có: \(\frac{1}{101}>\frac{1}{150}\)

\(\frac{1}{102}>\frac{1}{150}\)

.........................

\(\frac{1}{150}=\frac{1}{150}\)

\(\Rightarrow\frac{1}{101}+\frac{1}{102}+...+\frac{1}{150}>\frac{1}{150}+\frac{1}{150}+...+\frac{1}{150}=50.\frac{1}{150}=\frac{1}{3}\)(1)

Ta có:

\(\frac{1}{151}>\frac{1}{200}\)

\(\frac{1}{152}>\frac{1}{200}\)

...........................

\(\frac{1}{200}=\frac{1}{200}\)

\(\Rightarrow\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}=50.\frac{1}{200}=\frac{1}{4}\)(2)

Từ (1) và (2) ta có: 

\(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{150}+\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{3}+\frac{1}{4}=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}\)

                                                                                                                         đpcm