A. If x = lim n→∞ xn and y = lim n→∞ yn in a normed spaceV and α = lim n→∞ αn, show that x+y = lim n→∞ xn+yn and αx

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A. If x = lim n→∞ xn and y = lim n→∞ yn in a normed spaceV and α = lim n→∞ αn, show that x+y = lim n→∞ xn+yn and αx = lim n→∞ αnxn.

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A. If x= limx, and y = lim yn in a normed space V and a = n→∞⁰ n→∞o and axlim anxn. 00+11 lim an, show that x+y= limxn+Yn n→∞⁰ n→∞0