∑(n=1)(n-1)/(n!*2^n)
=∑(n=1)1/(n-1)!2^n)-∑(n=1)1/(n!*2^n)
=(1/2)∑(n=0)1/n!2^n-(∑(n=0)1/(n!*2^n)-1)
=(1/2)e^(1/2)-(e^(1/2)-1)
=1-(1/2)e^(1/2)