(1/[a(a+1)]+1/[(a+1)(a+2)])+(1/[(a+2)(a+3)]+1/[(a+3)(a+4)])=
=(a+2+a)/[a(a+1)(a+2)]+(a+4+a+2)/[(a+2)(a+3)(a+4)]=
(2a+2)[a(a+1)(a+2)]+(2a+6)/[(a+2)(a+3)(a+4)]=
=2(a+1)/[a(a+1)(a+2)]+2(a+3)/[(a+2)(a+3)(a+4)]=
=2/[a(a+2)]+2/[(a+2)(a+4)]=(2a+8+2a)/[a(a+2)(a+4)]=
=(4a+8)/[a(a+2)(a+4)]=4(a+2)/[a(a+2)(a+4)]=4/[a(a+4)]