Applying Number and Quantity to Everyday Life by Richardson Erik;

Author:Richardson, Erik;
Language: eng
Format: epub
Publisher: Cavendish Square Publishing LLC
Published: 2018-07-18T00:00:00+00:00

n = 2

(1 + 1/2)2 = 1.52

2.25

0.25

n = 4

(1 + 1/4)4 = 1.254

2.44141

0.19141

n = 10

(1 + 1/10)10 = 1.1010

2.59374

0.15233

n = 25

(1 + 1/25)25 = 1.0425

2.66584

0.07210

n = 50

(1 + 1/50)50 = 1.0250

2.69159

0.02575

n = 100

(1 + 1/100)100 = 1.01100

2.70481

0.01322

n = 1,000

(1 + 1/1,000)1,000 = 1.0011,000

2.71692

0.01211

As n approaches infinity (that just means as n o the value of calculating gets bigger), the fraction inside the parentheses gets smaller and smaller (1/10 versus 1/1000), and the sum inside the parentheses gets multiplied by itself more and more times.

Continuing this series out to n = 10,000 gives us a value of 2.71815. Notice how close that is to the value of calculating e out to 30 decimal places:

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