(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)quickly

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)quickly
(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕
(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)
quickly

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)quickly
(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
=1+2(1/2-1/3+1/3-1/4+...+1/1000-1/1001)
=1+2(1/2-1/1001)
=2000/1001
(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1))
=1/3(1-1/4+1/4-1/7+...+1/(3N-2)-1/(3N+1))
=1/3(1-1/(3N+1)
=(1/3)*(3N/(3N+1))
=N/(3N+1)

1/3*(54*a^2-64*a^3+6*(81*a^4-192*a^5)^(1/2))^(1/3)+16/3*a^2/(54*a^2-64*a^3+6*(81*a^4-192*a^5)^(1/2))^(1/3)-4/3*a