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BÀI 1:
\(N=\frac{2}{2.5}+\frac{2}{5.8}+...+\frac{2}{17.20}\)
\(N=2.\left(\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{17.20}\right)\)
\(N=2.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(N=2.\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(N=2.\frac{9}{20}\)
\(N=\frac{9}{10}\)
BÀI 2:
\(C=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3B=1.2.3+2.3.3+3.4.3+...+99.100.3\)
\(3B=1.2\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(3B=\left(1.2.3+2.3.4+3.4.5+...+99.100.101\right)-\left(1.2.3+2.3.4+...+98.99.100\right)\)
\(3B=99.100.101\)
\(3B=999900\)
\(\Rightarrow B=999900:3\)
\(B=333300\)
CHÚC BN HỌC TỐT!!!!
\(a,A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{90}\)
\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=3.\left(1-\frac{1}{10}\right)\)
\(A=3.\frac{9}{10}=\frac{27}{10}\)
\(b,B=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(B.\frac{3}{2}=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{17}\)
\(B=\frac{15}{34}:\frac{3}{2}=\frac{5}{17}\)
\(N=\dfrac{2}{3.6}+\dfrac{2}{6.9}+...+\dfrac{2}{2019.2022}\)
\(\Rightarrow N=2\left(\dfrac{1}{3.6}+\dfrac{1}{6.9}+...+\dfrac{1}{2019.2022}\right)\)
\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{3}{3.6}+\dfrac{3}{6.9}+...+\dfrac{3}{2019.2022}\right)\)
\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{2019}-\dfrac{1}{2022}\right)\)
\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2022}\right)\)
\(\Rightarrow N=\dfrac{2}{3}.\dfrac{673}{2022}\\ \Rightarrow N=\dfrac{673}{3033}\)