Question

[truc quynh]

Tính các tổng sau

B= 1 / 25.27 + 1 / 27.29 + 1 / 29.31 + ....... + 1 / 73.75

C= 4 / 2.4    + 4 / 4.6     + 4 / 6.8    + ........+ 4 / 2008.2010

        LÀM ƠN GIÚP MÌNH VỚI ĐƯỢC KO ..........HU HU

Answer 1

[Nguyễn Việt Hoàng]

\(\text{Ta có:}\) \(C=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(\Rightarrow\frac{1}{2}C=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2008.2010}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2008}-\frac{1}{2010}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{2010}\)

\(\Rightarrow\frac{1}{2}C=\frac{502}{1005}\)

\(\Rightarrow C=\frac{502}{1005}:\frac{1}{2}=\frac{1004}{1005}\)

Answer 2

[Dương Lam Hàng]

Ta có: \(B=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)

\(\Rightarrow2B=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)

\(\Rightarrow2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+....+\frac{1}{73}-\frac{1}{75}\)

\(\Rightarrow B=\left(\frac{1}{25}-\frac{1}{75}\right):2\)

\(\Rightarrow B=\frac{1}{75}\)

Vậy \(B=\frac{1}{75}\)

\(C=\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2008.2010}\)

\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\)

\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{2010}=\frac{502}{1005}\)

\(\Rightarrow C=\frac{502}{1005}:\frac{2}{4}=\frac{1004}{1005}\)

Vậy \(C=\frac{1004}{1005}\)

Ủng hộ tớ nha m.n ^_^