Question

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

• A. (1,0)
• B. (5,0)
• C. (1, 1/5)
• D. (5,1)

Answer 1

Answer:

B. (5,0)

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

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