tính 45.46 phần 410
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2.x}-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{45.46}=-2\)
\(\frac{1}{2.x}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{45.46}\right)=-2\)
\(\frac{1}{2.x}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{45}-\frac{1}{46}\right)=-2\)
\(\frac{1}{2.x}-\left(1-\frac{1}{46}\right)\)
\(\frac{1}{2.x}-\frac{45}{46}=-2\)
\(\frac{1}{2.x}=-2+\frac{45}{46}\)
\(\frac{1}{2.x}=\frac{-47}{46}\)
\(2x=\frac{46}{-47}\)
\(x=\frac{46}{-47}:2=\frac{-23}{47}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
= ( 45 x 46 + 46 x 48 + 48 ) x ( 48 x 52 + 3 x 52 - 47 x 48) x ( 45 x 126 + 45 x 2 - 90)
= ( 45 x46 + 46 x 45 + 46 x 3 + 48) x ( 48 x 47 + 48 x 5 + 3 x 52 - 47 x 48) x ( 45 x 42 x 2 + 90 - 90)
= ( 90 x 46 + 46 x 3 + 48) x ( 48 x 5 + 52 x 3 ) x ( 90 x 42)
= ( 90 x 46 + 186) x 396 x 3780
= 4326 x 396 x 3780
= 6475502880
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{45.46}\)
\(\Rightarrow S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{45.46}\)
\(\Rightarrow S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{45}-\frac{1}{46}\)
\(\Rightarrow S=1-\frac{1}{46}\)
\(\Rightarrow S=\frac{45}{46}\)
Bài làm
\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{45.46}\)
\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{45.46}\)
\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{45}-\frac{1}{46}\)
\(S=\frac{1}{1}-\frac{1}{46}\)
\(S=\frac{46}{46}-\frac{1}{46}\)
\(S=\frac{45}{46}\)
Vậy \(S=\frac{45}{46}\)
# Học tốt #
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2.x}-\frac{1}{1.2}-\frac{1}{2.3}-......-\frac{1}{45.46}=-2\)2
\(\frac{1}{2.x}-\left(\frac{1}{1.2}+\frac{1}{2.3}+.......+\frac{1}{45.46}\right)=-2\)
Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{45.46}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{45}-\frac{1}{46}\)
\(A=1-\frac{1}{46}=\frac{45}{46}\)
Ta có: \(\frac{1}{2.x}-\frac{45}{46}=-2\)
\(\frac{1}{2.x}=\frac{-47}{46}\)
\(\frac{-47}{-94.x}=\frac{-47}{46}\)
\(\Rightarrow x=\frac{-23}{47}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
45x\(\dfrac{46}{410}\)=\(\dfrac{207}{41}\).
\(\dfrac{45.46}{410}\)=\(\dfrac{207}{41}\)