Respuesta :

meeraasrinivas

Answer:

A. (1 + 1/26)²⁶

Step-by-step explanation:

[tex]e = \lim_{n \to \infty} (1+\frac{1}{n})^{n}[/tex]

and e ≈ 2.71828

The greater the value of n,the closer is the value of the expression (1+ 1/n)ⁿ to the value of e.

Of the given options, the greatest value of n = 26.

Hence (1 + 1/26)²⁶ is closer to the value of e.

alinakincsem

Answer:

The correct answer option is [tex](1+\frac{1}{26} )^{26}[/tex].

Step-by-step explanation:

We are given a few mathematical expressions and we are to figure out which one among them has the value closest to that of e.

Using a calculator, we can check that [tex]e[/tex] = 2.718281828.

So let's evaluate each one of our given expressions to check which one of them is the closest to e:

[tex](1+\frac{1}{26} )^{26}=2.667784966[/tex]

[tex](1+\frac{1}{25} )^{25}=2.665836331[/tex]

[tex](1+\frac{1}{23} )^{23}=2.661450119[/tex]

[tex](1+\frac{1}{24} )^{24}=2.663731258[/tex]

Therefore, by looking at the above calculated values, we can conclude that the value of [tex](1+\frac{1}{26} )^{26}[/tex] is the closest to the value of e.

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