Question

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+...+1/(19×21)=

кто сможет решить?
не всем это по силам​

Answer 1

1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)+1/(15*17)+1/(17*19)+1/(19*21) = 1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323+1/399

$\frac{1}{3} = \frac{1*4849845}{3*4849845} = \frac{4849845}{14549535}$

$\frac{1}{15} = \frac{1*969969}{15*969969} = \frac{969969}{14549535}$

$\frac{1}{35} = \frac{1*415701}{35*415701} = \frac{415701}{14549535}$

$\frac{1}{63} = \frac{1*230945}{63*230945} = \frac{230945}{14549535}$

$\frac{1}{99} = \frac{1*146965}{99*146965} = \frac{146965}{14549535}$

$\frac{1}{143} = \frac{1*101745}{143*101745} = \frac{101745}{14549535}$

$\frac{1}{195} = \frac{1*74613}{195*74613} = \frac{74613}{14549535}$

$\frac{1}{255} = \frac{1*57057}{255*57057} = \frac{57057}{14549535}$

$\frac{1}{323} = \frac{1*45045}{323*45045} = \frac{45045}{14549535}$

$\frac{1}{399} = \frac{1*36465}{399*36465} = \frac{36465}{14549535}$

НОЗ: 14549535

$\frac{4849845}{14549535}+\frac{969969}{14549535}+\frac{415701}{14549535}+\frac{230945}{14549535}+\frac{146965}{14549535}+\frac{101745}{14549535}+\frac{74613}{14549535}+\\\\\frac{57057}{14549535}+\frac{45045}{14549535}+\frac{36465}{14549535} = \frac{6928350}{14549535}$

Ответ: $\frac{6928350}{14549535}$