Question

[tran huyen nhu]

x-10/1.5-10/5.9-10/9.13-....-10/97.101=1

nhanh va giai chi tiet nhe!

Answer 1

[subjects]

\(x-\dfrac{10}{1\cdot5}-\dfrac{10}{5\cdot9}-\dfrac{10}{9\cdot13}-...-\dfrac{10}{97\cdot101}=1\\ x-\dfrac{10}{4}\cdot\left(\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\right)=1\\ x-\dfrac{10}{4}\cdot\left(\dfrac{1}{1}-\dfrac{1}{101}\right)=1\\ x-\dfrac{10}{4}\cdot\dfrac{100}{101}=1\\ x-\dfrac{250}{101}=1\\ x=1+\dfrac{250}{101}=\dfrac{351}{101}\)