4-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/90-21/110+23/132
=4-(1/2+1/3)+1/3+1/4-(1/4+1/5)+1/5+1/6-(1/6+1/7)+.-(1/10+1/11)+1/11+1/13
=4-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6+...+1/11+1/13
=4-1/2+1/13
=4-13/26+2/26
=4-11/26
=93/26