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a) \(\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)
\(=4.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\right)\)
\(=4.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=4.\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=4.\frac{32}{99}\)
\(=\frac{128}{99}\)
\(\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)
\(=2\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=2.\frac{32}{99}\)
\(=\frac{64}{99}\)
=6.3/2.5 +6.3/5.8+...+6.3/203.206
=6(3/2.5+3/5.8+...+3/203.206)
=6(1/2-1/5+1/5-1/8+...+1/203-1/206)
=6[(1/2-1/206)+(1/5-1/5)+(1/8-1/8)+...+(1/203-1/203)]
=6(1/2-1/206)=6(103/206-1/206)=6. 102/206=6. 51/103=306/103
A=6.( 3/2.5+3/5.8+...+3/203.206)
=6.(1/2-1/5+1/3-1/8+...+1/202-1/206)
=6.(1/2-1/206)=306/103
\(A=\dfrac{18}{2.5}+\dfrac{18}{5.8}+...+\dfrac{18}{203.206}\)
\(A=\dfrac{6.3}{2.5}+\dfrac{6.3}{5.8}+...+\dfrac{6.3}{203.206}\)
\(A=6\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+...+\dfrac{3}{203.206}\right)\)
\(A=6\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{203}-\dfrac{1}{206}\right)\)
\(A=6\left(\dfrac{1}{2}-\dfrac{1}{206}\right)\)
\(A=6.\dfrac{51}{103}\)
\(A=\dfrac{306}{103}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}+\frac{2}{99.101}\)
\(=1-\frac{1}{3}+\frac{!}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}=\frac{100}{101}\)
\(C=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{1024}+\frac{1}{2048}\)
\(\Rightarrow\)\(2C=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}+\frac{1}{1024}\)
\(\Rightarrow\)\(2C-C=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)
\(\Leftrightarrow\)\(C=1-\frac{1}{2048}=\frac{2047}{2048}\)
\(\frac{18}{2.5}+\frac{18}{5.8}+....+\frac{18}{103.106}\)
=\(6\left(\frac{3}{2.5}+\frac{3}{5.8}+....+\frac{3}{103.106}\right)\)
=\(6\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{103}-\frac{1}{106}\right)\)
=\(6\left(\frac{1}{2}-\frac{1}{106}\right)\)
=\(6.\frac{26}{53}\)
=\(\frac{156}{53}\)
\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{3}{5.7}+...+\dfrac{4}{97.99}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\left(1-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{98}{99}\)
\(=\dfrac{196}{99}\)
#NoSimp
=2(2/1*3+2/3*5+...+2/97*99)
=2(1-1/3+1/3-1/5+...+1/97-1/99)
=2*98/99=196/99
Ta có :
\(\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{97.99}\)
\(=\)\(2\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\right)\)
\(=\)\(2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=\)\(2\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=\)\(2.\frac{32}{99}\)
\(=\)\(\frac{64}{99}\)
Chúc bạn học tốt ~
\(C=\dfrac{4}{3\cdot5}+\dfrac{4}{5\cdot7}+\dots+\dfrac{4}{97\cdot99}\)
\(=2\cdot\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dots+\dfrac{2}{97\cdot99}\right)\)
\(=2\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dots+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\cdot\left(\dfrac{1}{3}-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{32}{99}=\dfrac{64}{99}\)
\(D=\dfrac{18}{2\cdot5}+\dfrac{18}{5\cdot8}+\dots+\dfrac{18}{203\cdot206}\)
\(=6\cdot\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dots+\dfrac{3}{203\cdot206}\right)\)
\(=6\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dots+\dfrac{1}{203}-\dfrac{1}{206}\right)\)
\(=6\cdot\left(\dfrac{1}{2}-\dfrac{1}{206}\right)\)
\(=6\cdot\dfrac{51}{103}=\dfrac{306}{103}\)
Khi đó: \(\dfrac{C}{D}=\dfrac{\dfrac{64}{99}}{\dfrac{306}{103}}=\dfrac{3296}{15147}\)