1/21+1/28+1/36+…+2/ x(x+1) giải hộ mình 11/10/2021 Bởi Arianna 1/21+1/28+1/36+…+2/ x(x+1) giải hộ mình
Đề là:$\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+…+\frac{2}{x(x+1)}=\frac{2}{9}$nhé bạn$⇔\frac{1}{3.7}+\frac{1}{4.7}+\frac{1}{4.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$ $⇔\frac{2}{2.3.7}+\frac{2}{2.4.7}+\frac{2}{2.4.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$ $\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$ $⇔2.(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+…+\frac{1}{x}-\frac{1}{x}+1)=\frac{2}{9}$ $⇔2.(\frac{1}{6}-\frac{1}{x}+1)=\frac{2}{9}$$⇔\frac{1}{x}+1=\frac{1}{6}-\frac{2}{9}$$⇔\frac{1}{x}+1=\frac{1}{18}$ $⇔x+1=18$$⇔x=17$ Bình luận
Đề là:$\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+…+\frac{2}{x(x+1)}=\frac{2}{9}$nhé bạn
$⇔\frac{1}{3.7}+\frac{1}{4.7}+\frac{1}{4.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$
$⇔\frac{2}{2.3.7}+\frac{2}{2.4.7}+\frac{2}{2.4.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$
$\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+…+\frac{2}{x}.(x+1)=\frac{2}{9}$
$⇔2.(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+…+\frac{1}{x}-\frac{1}{x}+1)=\frac{2}{9}$
$⇔2.(\frac{1}{6}-\frac{1}{x}+1)=\frac{2}{9}$
$⇔\frac{1}{x}+1=\frac{1}{6}-\frac{2}{9}$
$⇔\frac{1}{x}+1=\frac{1}{18}$
$⇔x+1=18$
$⇔x=17$