Question

The value of which of these expressions is closest to e ?(1+1/31)to the power of 31

(1 +1/32) to the power of 32
(1 +1/34) to the power of 34
(1+ 1/33) to the power of 33

Answer 1

Using a calculator, we can check that
`e=2.718281828`.

Lets evaluate each one of our expression the check which one is closest to
`e`:


`(1+ (1)/(31) )^(31)=2.675686306`


`(1+ (1)/(32))^(32)=2.676990129`


`(1+ (1)/(34) )^(34)=2.679355428`


`(1+ (1)/(33) )^(33)=2.678207651`

We can conclude that the value of (1 +1/34) to the power of 34 is the closest to the value of
`e`.