1,CMR:\(1-\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}-...-\dfrac{1}{1990}=\dfrac{1}{996}+\dfrac{1}{997}+\dfrac{1}{1990}\)
Những câu hỏi liên quan
1,CMR:
B,\(1-\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}-...-\dfrac{1}{1990}=\dfrac{1}{996}+\dfrac{1}{997}+\dfrac{1}{990}\)
1,CMR:\(1-\dfrac{1}{2}-\dfrac{1}{3}-...-\dfrac{1}{1990}=\dfrac{1}{996}+\dfrac{1}{997}+...+\dfrac{1}{990}\)
Chứng tỏ:
\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{1995}-\dfrac{1}{1996}=\dfrac{1}{996}+\dfrac{1}{997}+...+\dfrac{1}{1990}\)
Giúp Mình vs
\(\dfrac{1}{\begin{matrix}1\times&2\end{matrix}}+\dfrac{1}{\begin{matrix}2\times&3\end{matrix}}+\dfrac{1}{\begin{matrix}3\times&4\end{matrix}}+...........+\dfrac{1}{x\times\left(x+1\right)}=\dfrac{996}{997}\)
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{996}{997}\)
\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\)= \(\dfrac{996}{997}\) \(1-\dfrac{1}{x+1}\) = \(\dfrac{996}{997}\)
\(\dfrac{1}{x+1}\) = \(1-\dfrac{996}{997}\)
\(\dfrac{1}{x+1}\) =\(\dfrac{1}{997}\)
\(\Rightarrow\) x + 1 = 997
x = 997 - 1
x = 996
Vậy x = 996
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1,Chứng minh rằng:
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{1990^2}< \dfrac{3}{4}\)
2,Chứng minh rằng:
\(1< \dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}< 2\)
2) Mình nghĩ nên nhỏ hơn 3 thì dễ tính hơn... @@
Ta có :
\(\dfrac{x}{x+y+z}< \dfrac{x}{x+y}< \dfrac{x}{x}\\ \dfrac{y}{x+y+z}< \dfrac{y}{y+z}< \dfrac{y}{y}\\ \dfrac{z}{x+y+z}< \dfrac{z}{z+x}< \dfrac{z}{z}\)
\(\Rightarrow\dfrac{x}{x+y+z}+\dfrac{y}{x+y+z}+\dfrac{z}{x+y+z}< \dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}< \dfrac{x}{x}+\dfrac{y}{y}+\dfrac{z}{z}\\ \Rightarrow\dfrac{x+y+z}{x+y+z}< \dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}< 1+1+1\\ \Rightarrow1< \dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}< 3\)
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\(2+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{x.\left(x+1\right)}=1\dfrac{1989}{1990}\)
\(2+\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{2.\left(x+1\right)}=1\dfrac{1989}{1990}\)
làm nhanh nhé
\(M=\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{1990^2}\)
C/M : \(M< \dfrac{3}{4}\)
Tính \(\left(1+\dfrac{1}{1+2}\right)\times\left(1+\dfrac{1}{1+2+3}\right)\times\left(1+\dfrac{1}{1+2+3+4}\right)\times...\times\left(1+\dfrac{1}{1+2+3+...+997}\right)\)
1. Cho Ndfrac{1}{31}+dfrac{1}{32}+...+dfrac{1}{60}CMR dfrac{3}{5} N dfrac{4}{5}2. Cho Mdfrac{1}{3}-dfrac{2}{3^2}+dfrac{3}{3^3}-dfrac{4}{3^4}+...+dfrac{29}{3^{29}}-dfrac{30}{3^{30}}CMR M dfrac{3}{16}3. Cho Qdfrac{2}{3}+dfrac{8}{9}+dfrac{26}{27}+...+dfrac{3^{2021}-1}{3^{2021}}CMR Qdfrac{4041}{2}
Đọc tiếp
1. Cho N=\(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}\)
CMR \(\dfrac{3}{5}< N< \dfrac{4}{5}\)
2. Cho M=\(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{29}{3^{29}}-\dfrac{30}{3^{30}}\)
CMR \(M< \dfrac{3}{16}\)
3. Cho Q=\(\dfrac{2}{3}+\dfrac{8}{9}+\dfrac{26}{27}+...+\dfrac{3^{2021}-1}{3^{2021}}\)
CMR \(Q>\dfrac{4041}{2}\)