Найдите значения выражения:а) 1/6+1/12+1/20+...+1/380б) 2/15+2/35+2/63+...+2/323. Created by HadiRep3. matematika-ru

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July 2022 1 9 Report

Найдите значения выражения:
а) 1/6+1/12+1/20+...+1/380
б) 2/15+2/35+2/63+...+2/323

Answers & Comments

let5 $\frac{1}{6} + \frac{1}{12} + \frac{1}{20} +...+ \frac{1}{380} = \frac{1}{2*3} + \frac{1}{3*4} + \frac{1}{4*5} +...+ \frac{1}{19*20}=\\= \frac{1}{2} - \frac{1}{3} + \frac{1}{3} -\frac{1}{4} + \frac{1}{4} - \frac{1}{5} +...+ \frac{1}{18} - \frac{1}{19} + \frac{1}{19} - \frac{1}{20} = \frac{1}{2} - \frac{1}{20} = \frac{9}{20}=\\=0,45$

$\frac{2}{15} + \frac{2}{35} + \frac{2}{63} +...+ \frac{2}{323} = \frac{2}{3*5} + \frac{2}{5*7} + \frac{2}{7*9} +...+ \frac{2}{17*19} =\\= \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} +...+ \frac{1}{15} - \frac{1}{17} + \frac{1}{17} - \frac{1}{19} = \frac{1}{3} - \frac{1}{19} = \frac{16}{57}$

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