Let {xn} be a sequence of real numbers. Let yn be the average of the first n-terms: x1+ x2 + Yn + Xn n Prove that if {Xn} converges to x, then {Yn} also converges to xo. (Hint: using the definition of convergence, choose a large threshold N after which |xn – x| is as small as we want, then choose n large enough such that the |x; – x|/n is very small for 1 < i< N.)

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