Đề: \( \dfrac{ 1 ^ { 2 } \times a ^ { 3 } }{ a ^ { ^ { 2 } } \times 1 ^ { 2 } } \)
\(=\dfrac{1\times a^3}{a^2\times1}\)
\(=\dfrac{a^3}{a^2}\)
\(=\dfrac{a^1}{1}\)
\(=a\)
Tính :
a) A= \(\dfrac{1}{2010.2009}-\dfrac{1}{2009.2008}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
b) B= 63.(-124)-124.(-37)+(\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{11}\)).(-66)
Giúp mình với ạ! Mình cần gấp lắm
a) tính : \(B=\dfrac{2.1+1}{\left(1\left(1+1\right)\right)^2}+\dfrac{2.2+1}{\left(2\left(2+1\right)\right)^2}+....+\dfrac{2.99+1}{\left(99.\left(99+1\right)\right)^2}\)
b) cho \(3a^2+b^2=4ab\). tính giá trị biểu thức \(P=\dfrac{a-b}{a+b}\)
c)cho \(N=0,7.\left(2007^{2009}-2013^{1999}\right)\). CMR N là 1 số nguyên
a) \(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}\)\(-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
b)\(\dfrac{1}{99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-\dfrac{1}{97.96}-.....-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
c) \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+.....+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}+......+\dfrac{1}{255.257}\)
\(\dfrac{1}{50}-\dfrac{1}{50.49}-\dfrac{1}{49.48}-...-\dfrac{1}{2.1} \)
\(\dfrac{-1}{99}\dfrac{1}{99.98}-\dfrac{1}{98.97}-\dfrac{1}{97.96}-...\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
Tính
a)\(P=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{16}\left(1+2+3+...+16\right)\)
b)Cho a + b + c =2010 và \(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{c+a}=\dfrac{1}{3}\) Tính \(S=\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\)
Cho \(A=1 +\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2^{2023}-1}\) CMR: \(A>\dfrac{2023}{2}\)
Cho A=\(\dfrac{1}{2^2}+\dfrac{2}{2^3}+\dfrac{3}{2^4}+...+\dfrac{2016}{2^{2017}}\)
Chứng Minh A<1
Tính các số hữu tỉ sau:
A=\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{n+1}\right),n\)là số tự nhiên
B=\(\dfrac{1}{2000.1999}-\dfrac{1}{1999.1998}-\dfrac{1}{1998.1997}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
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