Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Show that the sequence whose n th term is given
by a n = 
is monotonically increasing.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. If we proceed numerically, we note that the terms of the sequence are a 1 = 
, a 2 = 
, a 3 = 
,……….
We note that, a 2 > a 1 , a 3 > a 2 and so on. A formal proof will be as follows we have a n+1 = 
Then, a n+1 –a n = 
– 
= 
> 0
( n is a natural number)
⇒ a n+1 –a n > 0 for all n.
Thus the sequence {a n } is monotonically increasing.
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