## 1/3.4 + 1/4.5+…+1/x.(x+1)=3/10 Tìm x

Question

1/3.4 + 1/4.5+…+1/x.(x+1)=3/10
Tìm x

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2 tháng 2021-05-05T17:38:51+00:00 2 Answers 5 views 0

1. $<=>\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+…+\dfrac{1}{x\left(x+1\right)}=\dfrac{3}{10}$

$<=>\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+…+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{3}{10}.$

$<=>\dfrac{1}{3}+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\left(\dfrac{1}{6}-\dfrac{1}{6}\right)+…+\left(\dfrac{1}{x}-\dfrac{1}{x}\right)-\dfrac{1}{x+1}=\dfrac{3}{10}$.

$<=>\dfrac{1}{3}+0+0+0+…+0-\dfrac{1}{x+1}=\dfrac{3}{10}.$

$<=>\dfrac{1}{3}-\dfrac{1}{x+1}=\dfrac{3}{10}.$

$<=>\dfrac{1}{x+1}=\dfrac{1}{3}-\dfrac{3}{10}.$

$<=>\dfrac{1}{x+1}=\dfrac{10}{30}-\dfrac{9}{30}.$

$<=>\dfrac{1}{x+1}=\dfrac{1}{30}.$

$\Rightarrow x+1=30.$

$\Rightarrow x=30-1=29.$

$Vậy x=29.$

2. $\text{Đáp án + Giải thích các bước giải:}$

(1)/(3.4)+(1)/(4.5)+…+(1)/(x.(x+1))=(3)/(10) (ĐK:x\ne{0;-1})

=>(1)/(3)-(1)/(4)+(1)/(4)-(1)/(5)+….+(1)/(x)-(1)/(x+1)=(3)/(10)

=>(1)/(3)-(1)/(x+1)=(3)/(10)

=>(1)/(x+1)=(1)/(3)-(3)/(10)

=>(1)/(x+1)=(1)/(30)

=>x+1=30

=>x=29(TM)`