Using a Summation Series to Estimate a Quantity
Say the only tool given to you is a calculator which performs addition, subtraction, multiplication, and division.
Let X= Summation (k=1 -->n) e^-(k/n)^2 with N^20
Explain a practical way of computing X within an error of 10^8. Roughly how big is X?
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Say the only tool given to you is a calculator which performs addition, subtraction, multiplication, and division.
Let , N = 1020.
Explain a practical way of computing X within an error of 10^8. Roughly how big is X?
Solution:
We will start by remembering one of the definitions of Riemann integral, when the integration interval is (0, 1) and this is covered by an uniform division:
( 1)
If we consider now
( 2)
we will have
( 3)
Thus, for N = big enough, we can state the evaluation:
...
Solution Summary
A Summation Series is used to Estimate a Quantity. The solution is detailed and well presented.