What is the limit as n approaches 2 of (n+1/n)^n ?

The limit as n approaches 2 of (n+1/n)^n is 25/4

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limit as n approaches 2 of (n+1/n)^n

n \to 2 lim ((n + \frac{1}{n})^{n})

\frac{25}{4}

Decimal Notation

6.25

Solution steps

n \to 2 lim ((n + \frac{1}{n})^{n})

Plug in the value

n = 2

= (2 + \frac{1}{2})^{2}

Simplify

(2 + \frac{1}{2})^{2} : \frac{25}{4}

= \frac{25}{4}

\int (x^{2} + x) e^{- x} d x

(e^{x} + 2 x y^{2}) d x + 2 x^{2} y d y = 0

\int 3 x 3 x^{2} + 4 d x

\int \frac{( 2 x )}{( x - 2 ) ( x + 1 )} d x

\frac{\partial}{\partial x} (x \cdot e^{x^{2} - 4})

What is the limit as n approaches 2 of (n+1/n)^n ?
The limit as n approaches 2 of (n+1/n)^n is 25/4