1/6(lg1/2+lg1+lg2+lg4+lg8+……+lg1024)*log2(10)
=1/6(lg2^-1+lg2^0+lg2^1+lg2^2+lg2^3+.+lg2^10)*(1/lg2)
=1/6(-1+0+1+2+3+.+10)lg2*1/lg2
=1/6*44
=22/3