66   Life Contingencies

=vx+3lx+;— 1 dlx+ lx+§ dx

=vx+, (lx ~x+1~ approximately = vx+ld

x

=(1+i)ICx

or   Cx = (1 +1-i) Cx, approximately,

and   Aix = (1+i)Mx approximately

so that   Ax = lax   (1+ )Mx = (1 { i)Ax. Dx

co   1   co   1   co

14. We have ax = v`apx .dt = lx ov`lx+a . dt = Dx ~Dx+a . dt. 0

jNow, if we call   vx+`lx+a .dt = Dx

0

and put Nx for Dx+Dx+i+Dx+2+ .. . it follows that a =   

x Nx

Dx

('

Since Dx=J Dx+t.dt,

Dx is given in practical work its approximate value

Dx+§ = 2 (Dx +Dx+1) •

So that   -.A-.Tx = (Dx +Dx+1) +z (Dx+1 +Dx+2) + = z Dx +Dx+1 +Dx+2 + • • •

= 2Dx+Nx

=Nx — 2Dx

and   ax ='D"+Nx =+a, as before. Dx

0