chung minh rang 1/2+2/3+3/4+ ....+99/100<1
nhanh minh tick
Chung minh rang A=\(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{99}}+\frac{1}{\sqrt{100}}>10\)>10
chung minh rang 1-1/2+1/3-1/4+...+1/99-1/200=1/101+1/102+...+1/199+1/200
Chung minh 1/1!+2/3!+3/4!+4/5!+...+99/100!<1
chung minh rang \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{99}}>\sqrt{99}\)
Cho A= 1/2 . 3/4 . 5/6 . ......... . 99/100
B= 2/3 . 4/5 . ......... . 100/101
Chung minh A<B
cho C=\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)chung minh rang C>\(\frac{1}{2}\)
1/ Cho A= \(\dfrac{1}{3}\)-\(\dfrac{2}{3^2}\)+\(\dfrac{3}{3^3}\)-\(\dfrac{4}{3^4}\)+.....+\(\dfrac{99}{3^{99}}\)-\(\dfrac{100}{3^{100}}\) Chứng minh A < \(\dfrac{3}{16}\)
2/ Cho B=(\(\dfrac{1}{2^2}\)-1)(\(\dfrac{1}{3^2}\)-1)....(\(\dfrac{1}{100^2}\)-1) So sánh B và \(\dfrac{-1}{2}\)
Chứng minh rằng :100- ( 1+1/2+1/3+...+1/100)=1/2+2/3+3/4+...+99/100
