Consider a positive integer n=a₁a₂...a_k, k≥2. A trunk of n is a number of the form a₁a₂...a_t, 1≤t≤k-1. (For example, the number 23 is a trunk of 2351)

By T(n) we denote the sum of all trunks of n and let S(n)=a₁+a₂+...+a_k. Prove that n=S(n)+9T(n)