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In this paper, we prove the following result by perturbation technique. If <i>q</i> is a quasinilpotent element of a Banach algebra and spectrum of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>+</mo> <mi>q</mi> </mrow> </semantics> </math> </inline-formula> for any other quasinilpotent <i>p</i> contains at most <i>n</i> values then <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>q</mi> <mi>n</mi> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>. Applications to C* algebras are given.