a: \(=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\right)\)
\(=5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=5\cdot\dfrac{30}{31}=\dfrac{150}{31}\)
b: \(=\dfrac{2\left(1-\dfrac{1}{19}+\dfrac{1}{43}-\dfrac{1}{1943}\right)}{3\left(1-\dfrac{1}{19}+\dfrac{1}{43}-\dfrac{1}{1943}\right)}=\dfrac{2}{3}\)
`a,1/5 A = 5/(1.6) + 5/(6.11) + ... + 5/(26.31)`
`1/5A = 1/1 - 1/6 + 1/6 - 1/11 + ... + 1/26 - 1/31`
`1/5 A=30/31`
`A = 150/31`
`B = (2. (1 - 1/19 + 1/43 - 1/1943))/(3 . (1 - 1/19 + 1/43 - 1/1943))`
`= 2/3`
