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August 27, 2021 4:34 pm 30 pts
Example. Let lal< 1, then lim an = 0. n-00 Suppose a 0, because lim a = 0 is clear for a = 0. Since la <1, we can write al 1b where b > 0. By the binomial theorem (1+b =1+ nb + + b" 21+ nb > nb, 2 1 la-o-ld+by nb 1 SO 1 Now consider e >0 and let N =- . Then if n> N, we haven> and hence Jan- 0<- eb &b DMI NOTE 8 PRO QUAb'EAMERA n=1.
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