# the expression 1/50 (1/50 +2/50+ 3/50+ .....50/50)is a Reimann sum approximation for

(everything in the parantheses is square root except the 1/50 outside the paratheses)

the answer has to me the integral form so from looking at the formula in my book i got:

1/50 * integral(from 0 to 50) square root x dx

hopefully i wrote the expression right in words correctly. tell me if it is confusing and i write it in different words .

My only concern with this answer is why is it from 0 to 50 isnt 50/50 1 not 50. That is my only discrepancy with your solution. so woulnt it be form 0 to 1? Im just asking

## for clarification.

Yes, you are correct. The expression should be 1/50 * integral(from 0 to 1) square root x dx.

## The expression you provided can be interpreted as a Riemann sum approximation for the integral. Let's go through the steps to clarify:

We have the expression: 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50)

This can be written as: 1/50 * (1/50 + 2/50 + 3/50 + ... + 50/50)

Now, let's express the terms within the parentheses in terms of x:

1/50 * (sqrt(1/50) + sqrt(2/50) + sqrt(3/50) + ... + sqrt(50/50))

Simplifying the expression inside the parentheses:

1/50 * (sqrt(1)/sqrt(50) + sqrt(2)/sqrt(50) + sqrt(3)/sqrt(50) + ... + sqrt(50)/sqrt(50))

Now, we can rewrite this expression in integral form. The integral of the square root of x is ∫√x dx.

Let's substitute:

1/50 * (sqrt(1)/sqrt(50) + sqrt(2)/sqrt(50) + sqrt(3)/sqrt(50) + ... + sqrt(50)/sqrt(50))

= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)

= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)

= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)

= (1/50) * ∫(√1 + √2 + √3 + ... + √50) dx

Now, let's consider the limits of integration. Since the expression is summing terms up to 50, it is appropriate to integrate from 0 to 50.

Therefore, we can rewrite the expression as:

(1/50) * ∫(√1 + √2 + √3 + ... + √50) dx, integrated from 0 to 50.

I hope this clarifies the steps for you. If you still have any questions, feel free to ask!

## From your explanation, it seems that you have correctly identified the Riemann sum approximation and the integral form. However, there seems to be a misunderstanding regarding the limits of integration.

Let's break down the expression step by step to clarify:

1. The expression you provided is: 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50).

This can be simplified as: 1/50 * (sum of (n/50) from n = 1 to 50).

2. Recognizing that the sum of (n/50) from n = 1 to 50 is simply the sum of the integers from 1 to 50 divided by 50, we get:

1/50 * (1/50 + 2/50 + 3/50 + ... + 50/50) = 1/50 * (1 + 2 + 3 + ... + 50)/50.

3. Simplifying further, we have: 1/50 * (sum of integers from 1 to 50)/50.

The sum of integers from 1 to 50 can be calculated as (50 * 51) / 2 = 1275.

Therefore, the expression becomes: 1/50 * 1275/50.

4. Now, addressing your concern about the limits of integration:

The integral form of the expression should have the limits corresponding to the range of the sum, which is from 1 to 50.

Hence, the integral should be from 1 to 50, not 0 to 50.

To summarize, the expression 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50) can be written as the integral:

∫(1/50)√(x) dx, with the limits of integration being from 1 to 50.