Question

1+1/2+1/6+1/12+1/20+1/30+.+1/90 简便计算 2/3+2/15+2/35+2/63+2/99

Answer 1

1+1/2+1/6+1/12+1/20+1/30+.+1/90 简便计算

=1+1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10

=1+1/2+1/2-1/10

=19/10;

2/3+2/15+2/35+2/63+2/99+2/143 简便计算

=2/3+(1/3-1/5)+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13

=1-1/13

=12/13;

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