đặt \(A=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{630}\)
\(A=\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{1260}\)
\(A=2\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{35\cdot36}\right)\)
\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{35}-\frac{1}{36}\right)\)
\(A=2\left(1-\frac{1}{36}\right)\)
\(A=2\cdot\frac{35}{36}\)
\(A=\frac{35}{18}\)
ok Đặt A = 1/3 + 1/6 + 1/10 + ... + 1/630
Ta có : 1/2A = 2/6 + 2/12 + 2/20 + ... + 2/1260
1/2A = 2/2.3 + 2/3.4 + 2/4.5 + ... + 2/35.36
1/2A = 2 ( 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/35.36 )
1/2A = 2 ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/35 - 1/36 )
1/2A = 2 ( 1/2 - 1/36 )
1/2A= 2. 17/36
1/2A = 34/36
A = 34/36 : 1/2
A = 17/9
=> 1 + 17/9
= 26/9
ko chắc đúng
