How to prove that #{1/2^n}# is bounded series ?

1 Answer
Wataru
Apr 13, 2017

#{1/2^n}# is bounded since #0<1/2^n leq1/2#.

Explanation:

For all natural number #n#,

(a) #0 < 2^n Rightarrow 0 < 1/2^n#

(b) #n geq 1 Rightarrow2^n geq 2^1 Rightarrow 1/2^n leq 1/2^1#

So, #0<1/2^n leq 1/2# for all natural number #n#

Hence, #{1/2^n}# is bounded.

I hope that this was clear.

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