limit of (1+2/n)^n || step by step Explanation: convergence and divergence

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?

limit of (1+2/n)^n || Step by Step Explanation

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)  a                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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