cho B=1+\(\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{x}\left(1+2+3+...+x\right)\)

tính \(B=-\dfrac{1}{3}+\dfrac{1}{3}^2-\dfrac{1}{3}^3+...+\dfrac{1}{3^{50}}-\dfrac{1}{3^{51}}\)

cho các số \(0< a_1< a_2< a_3< ...< a_{15}\) chứng mình rằng \(\dfrac{a_1+a_2+a_3+...+a_{15}}{a_5+a_{10}+a_{15}}< 5\)