[tex]a=\sqrt{2(1+2+3+...+50) * ( \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} + ...+ \frac{1}{50*51} ) } [/tex]
[tex]a = \sqrt{2(50*51:2) * ( \frac{2-1}{1*2} + \frac{3-2}{2*3} + \frac{4-3}{3*4} + ...+ \frac{51-50}{50*51}) } [/tex]
[tex]a = \sqrt{50*51(\frac{2}{1*2} - \frac{1}{1*2} + \frac{3}{2*3} - \frac{2}{2*3} + ...+ \frac{51}{50*51} - \frac{50}{50*51} ) } [/tex]
[tex]a = \sqrt{50*51(\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ...+\frac{1}{50} - \frac{1}{51} ) } } [/tex]
[tex]a = \sqrt{50*51 (\frac{1}{1} - \frac{1}{51}) } [/tex]
[tex]a = \sqrt{50*51*\frac{50}{51} } [/tex]
[tex]a = \sqrt{50^{2} } = 50[/tex]
