1.
1=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9
-1/10+1/10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+1/10每兩個(gè)分成一組
=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10
這是數(shù)列中的列項(xiàng)相消法
2.等比數(shù)列法
1=1/2+1/4+1/8+1/16+1/32+1/32[還只有6項(xiàng),再拆]
1/2=3/6=1/6+2/6=1/6+1/3
1/4=5/20=1/20+4/20=1/20+1/5
1/8=9/72=3/72+6/72=1/24+1/12
1/32=3/96=1/96+2/96=1/96+1/48
代入
1=1/6+1/3+1/20+1/5+1/24+1/12+1/16+1/32+1/96+1/48
從無到有,再拆項(xiàng),降低難度,再做,這也是做數(shù)學(xué)題的不變真理