简便计算:9.99x22.2+33.3x3.34 1/3+1/15+1/35+1/63+1/99+1/143

题目

简便计算:9.99x22.2+33.3x3.34 1/3+1/15+1/35+1/63+1/99+1/143

答案

9.99x22.2+33.3x3.34
=0.3x33.3x22.2+33.3x3.34
=33.3x(0.3x22.2+3.34)
=33.3x(6.66+3.34)
=33.3x10
=333
1/3+1/15+1/35+1/63+1/99+1/143
=1/3+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)+1/(11x13)
=1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+1/2*(1/9-1/11)+1/2*(1/11-1/13)
=1/3+1/6-1/26
=1/2-1/26
=13/26-1/26
=6/13