Question

Tìm x biết: \(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\right)x=\frac{22}{45}\)

Answer 1

=>(2/1.2.3+2/2.3.4+....+2/8.9.10).x=22/45

=>(1/1.2-1/2.3+1/2.3-1/3.4+....+1/8.9-1/9.10).x=22/45

=>(1/1.2-1/9.10).x=22/45

=>22/45.x=44/45

=>x=2

Answer 2

4+2^2+2^3+....+2^20=2^n

=>2^2+2^2+2^3+....+2^20=2^n

đặt 2^2+2^3+....+2^20

=>2A-A=2^21-2^2

khi đó A=2^2+2^21-2^2=2^21=2^n

=>n=21

Answer 3

2.(4+2^2+2^3+2^4+...+2^20)=2^3+2^3+2^4+2^5+...+2^21=>4+2^2+2^3+...+2^20=2^3+2^4+2^5+...+2^21-(4+2^2+2^3+2^4+...+2^20)=2^21-2^2-4=2097144