40分之1加56分之1加上72分之1加上90分之1加上110分之1加上132分之1等于多少?

1/40+1/56+1/72+1/90+1/110+1/132
=1/40+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)+1/(11*12)
=1/40+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/40+1/7-1/12
=(21+120-70)/840
=71/840
【备注1/40如果是1/42】
1/42+1/56+1/72+1/90+1/110+1/132
=1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)+1/(11*12)
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/6-1/12
=1/12