Question

tìm x biết:

                        ( 1/2+ 1/4+ 1/8+ 1/16 ) : x = 1/2 + 1/6 + 1/12 + 1/20 + ....+ 1/132

 

                                                         giup minh nha cac ban

Answer 1

Xét: 

A = 1/2 + 1/4 + 1/8 + 1/16

2A = 1 + 1/2 + 1/4 + 1/8

2A - A = 1 - 1/16

=> A = 15/16

Xét: 

B = \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)

B = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\)

B = \(1-\frac{1}{1}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{11}-\frac{1}{12}\)

B = \(1-\frac{1}{12}\)

=> B = \(\frac{11}{12}\)

Thay vào, ta có:

\(\frac{15}{16}:x=\frac{11}{12}\)

=> \(x=\frac{15}{16}:\frac{11}{12}\)

=> \(x=\frac{45}{44}\)