Question

一道简算题

1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110

Answer 1

根据
1/（a*b）=1/a-1/b
可解
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110
解：原式=1/（2*3）+1/（3*4）+1/（4*5）+……+1/（10*11）
=1/2-1/3+1/3-1/4+……+1/10-1/11
=1/2-1/11
=11/22-2/22
=9/22

Answer 2

解：原式=1/(2*3)+1/(3*4)+...+1/(10*11)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/10-1/11)
=1/2-1/11
=9/22

Answer 3

1/(2*3)+1/(3*4）+1/(4*5)+……+1/(10*11)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/10-1/11
=1/2-1/11
=9/22

Answer 4

原式=1/（2*3）+1/（3*4）+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5……+1/9-1/10+1/10-1/11
=1/2-1/11
=9/22

Answer 5

解: 原式= 1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10+1/10×11

=1/2-1/3+1/3-1/4+1/4...-1/10+1/10-1/11
=1/2-1/11
=9/22