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+2/143 简便计算

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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Answer 2

1+1/2+1/6+1/12+1/20+1/30+......+1/90
=1 + 1/(1×2) + 1/(2×3) + 1/(3×4) + 1/(4×5) + ...... + 1/(9×10)
=1 + (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ...... + (1/9 - 1/10)
=1 + (1/1 - 1/10)
= 19/10

2/3+2/15+2/35+2/63+2/99+2/143
=2/(1×3) + 2/(3×5) + 2/(5×7) + 2/(7×9) + 2/(9×11) + 2/(11×13)
=(1 - 1/3) + (1/3 - 1/5) + ...... + (1/11 - 1/13)
= 1 - 1/13
= 12/13

Answer 3

解1+1/2+1/6+1/12+1/20+1/30+......+1/90
=1+（1-1/2）+（1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+......+(1/9-1/10)
=1+1-1/10
=19/10
2/3+2/15+2/35+2/63+2/99+2/143
=2*(1/3)+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