S1=sin(π/7)>0,
S2=sin(π/7)+sin(2π/7)>0
S3=sin(π/7)+sin(2π/7)+sin(3π/7)>0,
S4=sin(π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)>0,
S5=sin(π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)+sin(5π/7)>0
S6=sin(π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)+sin(5π/7)+sin(6π/7)>0
S7=sin(π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)+sin(5π/7)+sin(6π/7)+sin(π)>0,
S8=sin(1π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)+sin(5π/7)+sin(6π/7)+sin(π)+sin(8π/7)
=sin(1π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)+sin(5π/7)>0
S9=sin(1π/7)+sin(2π/7)+sin(3π/7)+sin(4π/7)>0
S10=sin(1π/7)+sin(2π/7)+sin(3π/7)>0
S11=sin(1π/7)+sin(2π/7)>0
S12=sin(1π/7)>0
S13=0
S14=0+sin(2π）=0
……
在S1,S2,…,S100中,为0的项共有14项,其余项都为正数．
故在S1,S2,…,S100中,正数的个数是86．