上面的是合起来,你可以用拆分呀
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=1+1/7
=8/7
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=1-1/7
=6/7
已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5
计算1+1/2-5/6+7/12-9/20+11/30-13/42。
请仔细观察上面的规律,再利用规律计算。
裂项法
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7
=1-1/7
=6/7
1/2+1/4+1/8= 1-1/2+1/2-1/4+1/4-1/8=1-1/8=7/8
1/2+1/4+1/8+1/16= 1-1/2+1/2-1/4+1/4-1/8+1/8-1/16=1-1/16=15/16
1/2+1/4+1/8+1/16+1/32= 1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32=1-1/32=31/32
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=1-1/256=255/256
=0
看成a*a+1/2*a-a*b
=a*(a-1/2)-a*b
=a*b-a*b
=0
1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)=1-1/8=7/8
你把加号写成等号了,是不是
解:1/2+1/6+1/12+1/20=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5=1-1/5=4/5
1/2*3+1/3*4+1/4*5......+1/99*100
=1/2-1/3+1/3-1/4+1/4-1/5+......+1/99-1/100
=1/2-1/100
=49/100
利用前后两项相互抵消可得。