几道数学简算题(31+1/2+1/3+1/5)÷(1/2+1/3+1/5)(19/96+1919/9696+191919/969696)÷19191919/96969696)21-4/3-4/15-4/35-4/63-4/99-4/143-4/195-4/225

Question

几道数学简算题
(31+1/2+1/3+1/5)÷(1/2+1/3+1/5)
(19/96+1919/9696+191919/969696)÷19191919/96969696)
21-4/3-4/15-4/35-4/63-4/99-4/143-4/195-4/225

Answer 1

(31+1/2+1/3+1/5)÷(1/2+1/3+1/5)＝31÷(1/2+1/3+1/5)+1＝31÷(31/30)+1=31
(19/96+1919/9696+191919/969696)÷19191919/96969696)
= 19/96*(1+101/101+10101/10101)÷19/36(1010101/1010101)=3
21-4/3-4/15-4/35-4/63-4/99-4/143-4/195-4/225
=21-4(1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/225)
=21-4[1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)+1/(15*15)]
=21-4[(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)/2+(1/11-1/13)/2+(1/13-1/15)/2+1/225]
=21-4[(1-1/15)/2+1/225]=21-4(7/15-1/225)=21-416/225