Local higher derivations on C*-algebras are higher derivations

Let a be a banach algebra. we say that a sequence {dn}∞ n=0 of continuous operators form a into a is a local higher derivation if to each a ∈ a there corresponds a continuous higher derivation {da,n}∞ n=0 such that dn(a) = da,n(a) for each non-negative integer n. we show that if a is a c∗-algebra then each local higher derivation on a is a higher derivation. we also prove that each local higher derivation on a c∗-algebra is automatically continuous.