Question

Math Question Help.
A student wanted to find the sum of all the even numbers from 1 to 100. he said:

The sum of all the even numbers from 1 to 100 is twice the sum of all the odd numbers from 1 to 100.
The sum of all the odd numbers from 1 to 100 is 100^2.

Explain why each of these statements is incorrect.

Answer 1

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Answer 2

Where did you get that answer?

Answer 3

They never said the result was the sum of all the even numbers

Answer 4

Well what makes this problem wrong, is that all of the even numbers end up being this:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + ... - Anyhow, when you do add them all up it equals: 2,550, however all of the even numbers added together equals: 2,500, so the sum of all of the even numbers equals 2,550 which isn't double the odd numbers which ended up equaling 2,500.
Now why would the last one be wrong? You know that both sums equal roughly 2,500, which I thought that both would have equaled roughly the same, anyhow... so how is the last statement wrong?

Answer 5

that was thorough

Answer 6

Thank you, I tend to be more thorough with my answers or responses.