Question

Tìm x :

a) 10 + 15 + 20 + ... + 300 + x = 6750

b) \(\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}-\frac{1}{x+1}=\frac{59}{77}\)

 

Answer 1

a)Ta đặt A=10+15+...+300

Số số hạng của A là:(300-10):5+1=59(số)

Tổng của A là:(10+300).59:2=9145

=>9145+x=6750

=>x=6750-9145

=>x=-2395

b)\(\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}-\frac{1}{x+1}=\frac{59}{77}\)

<=>\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{6.7}-\frac{1}{x+1}=\frac{59}{77}\)

<=>\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}-\frac{1}{x+1}=\frac{59}{77}\)

<=>\(1-\frac{1}{7}-\frac{1}{x+1}=\frac{59}{77}\)

<=>\(\frac{6}{7}-\frac{1}{x+1}=\frac{56}{77}\)

<=>\(\frac{1}{x+1}=\frac{6}{7}-\frac{56}{77}=\frac{66}{77}-\frac{56}{77}\)

<=>\(\frac{1}{x+1}=\frac{10}{77}\)

<=>10(x+1)=77

<=>10x+10=77

<=>10x=67

<=>x=6,7