# 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.