Câu hỏi của truc quynh

Question

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 MI...

Nguyễn Việt Hoàng · Accepted Answer

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

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

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

$\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{2010}$

$\Rightarrow\frac{1}{2}C=\frac{502}{1005}$

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

Câu trả lời:

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

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

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

$\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{2010}$

$\Rightarrow\frac{1}{2}C=\frac{502}{1005}$

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

Dương Lam Hàng · Answer

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 ^_^