If Un=[1+1/n]

Question

a.show that 2<Un<3
b.show that sequence Un is monotonic increasing
c.give reasons why sequence Un converges

Answer 1

as n gets large, Un → 1
(a) ?? so 1 < Un <= 2
(b) Un is decreasing
(c) you can find a value N so that UN < 1+ε for any ε>0

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