Question

The value of which of these expressions is closest to e?

A.(1+ 1/26)26
B.(1+1/25)25
C.(1+1/23)23
D.(1+24)24

Answer 1

The correct answer option is
`(1+(1)/(26) )^(26)`.

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
`e` = 2.718281828.

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

`(1+(1)/(26) )^(26)=2.667784966`

`(1+(1)/(25) )^(25)=2.665836331`

`(1+(1)/(23) )^(23)=2.661450119`

`(1+(1)/(24) )^(24)=2.663731258`

Therefore, by looking at the above calculated values, we can conclude that the value of
`(1+(1)/(26) )^(26)` is the closest to the value of e.

Answer 2

A. (1 + 1/26)²⁶

Explanation:

`e = \lim_(n \to \infty) (1+(1)/(n))^(n)`

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.