Chứng minh rằng:
\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
Chứng minh rằng: \(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{99}{100!}\)< 1
CMR: \(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{1}{2}\)
*Rút gọn
1) G=\(\dfrac{2}{3}+\dfrac{2}{3^3}+\dfrac{2}{3^5}+...+\dfrac{2}{3^{99}}\)
2) H=\(\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{16}}+...-\dfrac{1}{2^{58}}\)
3) E=\(\dfrac{-1}{3}+\left(\dfrac{-1}{3}\right)^2+\left(\dfrac{-1}{3}\right)^3+...+\left(\dfrac{-1}{100}\right)^{100}\)
\(A=\dfrac{1001}{1000^2+1}+\dfrac{1001}{1000^2+2}+\dfrac{1001}{1000^3+3}+.....+\dfrac{1001}{1000^2+100}\)Chứng minh rằng 1<A2<4
Chứng minh rằng :\(\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{99}}+\dfrac{1}{\sqrt{100}}\)>10
1/ Tính
\(\dfrac{\left(1+2+3+...+100\right).\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}}\)
2/ Tìm x:
\(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
3/ Cho \(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
Chứng minh: \(\dfrac{7}{12}< A< \dfrac{5}{6}\)
4/ Tìm \(a,b\varepsilon Q:a+b=a.b=a:b\)
Giúp mik nha mai mik cần rồi.
Cho B=\(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\). Chứng minh 1/15<B<1/10
A = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+......+\dfrac{1}{2^{100}}\)
B = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{100^2}\)
mk cần gấp
