b(n)=1/[n*2^n] - 1/[(n+1)*2^(n+1)]t(n)=1/[1*2]-1/[2*2^2]+1/[2*2^2]-1/[3*2^3]+...+1/[(n-1)*2^(n-1)] - 1/[n*2^n] +1/[n*2^n]-1/[(n+1)*2^(n+1)]=1/2 - 1/[(n+1)*2^(n+1)]
