# Eagerly waiting so plzz reply fast ..............in limits if e^n -1/n=1and we know that e has the value 2.7 so it is the constant does'nt it???so why not every constant has value 1 like1^n-1/n=1 why it is not possible???any queries about the question yeah you can ask me in comment section given below but ya i want an answer.............

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kya h??

2014-11-14T01:02:10+05:30

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Euler's number e is defined as follows:

Let n = mx = x/y. Use binomial expansion theorem,

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Let a = a positive real number,  like 1, e , 2

Now, choose a = 1,  then, you get :

If you choose a = e, then you get

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e^x is also defined using Taylor series as: e^x=1+x/1!+x^2/2!+....to infinity. This is not finite series. e^x-1 = x(1+x/2! +x^2/3!+..... to infinity. (e^x-1)/x = 1+x/2!+x^2/3!+....infinity, as x ->0, RHS = 1.