Could someone please check my work

Suppose That X,, X2, ..., In are real numbers. Prove That ( X, * * 2 + ... + Xn / = / X,1 + / *2/ + ... + / xn/using induction on n. * Generalized Triangle Base Case: Inequality Let PCn) be the statement ai s E lail , for all NEIN Then PCI) asserts That LHS = E a; ) = Jail = z | a, = /a,1 = RHS . LHS = 1Q, 1 = RHS Thus, PCI) is True, which establishes The basis for induction. Inductive step . K Assume That a; = = ail is True for Some KENN. K+ 1 K+ 1 WTS 1=1 K+ 1 LHS =/ 8 a; 1 1 1= 1 K saint anti 1 = 1 12 ail+ akti by Theorem 3.2.10 ( 2) for The Triangle inequality Use The assumption = = EJail + axel K+ 1 = E a; = RHS By The 3. 1.2, Hail = = Jail, for all n E IN