Show that the sequence a_n = (n+2)/(n+1) is monotonic decreasing and bounded below, and hence show that it converges.
Can someone help please?
Can someone help please?
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a_n
= (n + 2) / (n + 1)
= (n + 1 + 1) / (n + 1)
= 1 + 1/(n + 1)
=> as n increases, 1/(n+1) decreases
and hence a_n decreases monotonically.
Also, as n → ∞ 1/(n + 1) → 0 and a_n → 1
Thus, a_n is bounded below with a lower bound of 1.
= (n + 2) / (n + 1)
= (n + 1 + 1) / (n + 1)
= 1 + 1/(n + 1)
=> as n increases, 1/(n+1) decreases
and hence a_n decreases monotonically.
Also, as n → ∞ 1/(n + 1) → 0 and a_n → 1
Thus, a_n is bounded below with a lower bound of 1.