$S=\frac{5}{n},n∈N$ The least upper bound and greatest lower bound are ................. , ...............

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$S=\frac{5}{n},n∈N$ ന്യൂനതമ ഉപരി പരിബന്ധവും ഉച്ചതമ നീച പരിബന്ധവും ................. , ...............ആണ്.

A(1,0)

B(5,0)

C(1, 1/5)

D(5,1)

Answer:

inf S ≤ inf S₀ ≤ sup S₀ ≤ sup S

$S_0 ⊂ S$

S= (1 4)

$S_0 = (2,3)$

inf S₀ = 2 ; inf S ≤ inf S₀

inf S=1 ; sup S₀ ≤ sup S

Sup S₀ = 3

Sup S = 4

sup S = 5 ∈ S

inf S = 0 ∉ S

lim_{(n->∞)}\frac{5}{n}=0

$S=(5, \frac{5}{2}, \frac{5}{3}, \frac{5}{4}, 1 , \frac{5}{6}, \frac{5}{7} .....)$

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