Today we will learn how we can find the limit of (1+2/n)^n in an
easy way and in steps. In calculus, the limit of a function is an important
topic of mathematics. From that, we have taken to find the limit of (1+2/n)^n step by step.
How to find the limit of (1+2/n)^n as n goes to infinity?
To find the limit of (1+2/n)^n as n goes to
infinity you need to follow the following steps.
Step 1:
an=(1+2/n)^n
Step 2:
Take limit n→∞ on both sides
lim (n→∞) an = lim (n→∞ ) (1+2/n)^n
We know that,
lim (n→∞) [(1+b/n)n= e^b]
Hence, lim (n→∞) (1+2/n)^n will be
lim n→∞ e^2 ANS
Whether (1+2/n)^n is Convergence and Divergence?
To find whether (1+2/n)^n convergence and divergence. The simple is answer is that (1+2/n)^n is convergent because the limit of (1+2/n)^n≠∞
familiar questions with the limit (1+2/n)^n as n go to infinity.
We will study some familiar questions with the limit (1+2/n)^n. here is a question
(1+1/n)^6n. We will show you how to solve (1+1/n)^6n by
following the method of (1+2/n)^n.
Take limit n→∞ on both sides
lim (n→∞) an = lim (n→∞) (1+1/n)^6n
We know that,
lim (n→∞) [(1+y/n)n=
e^y]
write, (1+1/n)^6n as [(1+1/n)^n]^6
Hence, lim (n→∞) [(1+1/n)^n]^6
will be
lim n→∞ e^6 ANS
See Also: Prove that lim n→∞ (1+1/n)^mn=e^m
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