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Probability Level 3

Without using a calculator, find the value of ( 1.00142857 ) 700 (1.00142857)^{700} truncated to 2 decimal places,


The answer is 2.71.

Nippun Sharma by Nippun Sharma , 19, India

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1 solution

Nippun Sharma
Feb 20, 2017

The above problem can be broken down into the following form:

( 1 + 0.00142857 ) 700 (1+0.00142857)^{700}

Which is equal to,

( 1 + 1 / 700 ) 700 (1 + 1/700)^{700}

This expression is the general form of e e = = ( 1 + 1 / n ) n (1+1/n)^n

Therefore we could say that the expression is approximately equal to e e = = 2.71 2.71

2 Helpful 0 Interesting 0 Brilliant 0 Confused

For completeness, you would have to study the rate of convergence and ensure that we are close enough. For example, the 3 decimal place truncation is 2.716, whereas e ≈ 2.718 e \approx 2.718 .

Note that when rounded to 2 decimal places, the answer would be 2.72 (which is still accepted due to the 2% margin of error).

Calvin Lin Staff - 4 years, 3 months ago

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