After solving all 6 problems, I just remembered a very fast, easy and awesome way to solve other problems like these 6 problems. (Note: You can easily prove my equations!)
Back to our easy equations:
These are very simple right, I think you can prove them easily. But there is a question: Can you calculate quickly this sum:
My answer is: Yes, you can! But how?
Using this sum above
First, calculate the total terms of this sum:
Numbers of Terms .
In this equation, the number of terms is:
Our first step is completed, now move to the next step To sum this equation, use this: The sum
So in this equation: The sum is:
This is my solution, and you can use it in all arithmetic series. I hope to discuss more with all of you.