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That was nice.

On the same note, I want to know how to derive formulas for summation.

For Example: I know that the sum of first n positive integers is {n*(n+1)]/2. I also know how to prove it. But what I want to know how to derive this formula in the first place. Do I use integration or something else.

Same thing about sum of first n squares. How do I derive the formula in the first place?

I dont want the reverse proof , in which we already have the formula and go on to prove that it is correct.

Am I making any sense?

Is there any general rule for finding formulas for summation of a series? Or am i being too hopeful?

**makada**- Replies: 4

This is a nice problem i got from a friend:

"There are 50 oranges which are laid out on a straight road in a linear fashion. The distance between the the first and second orange is one meter, between the second and third is three meters, between the third and fourth is five meters, ... and so on. A large collecting basket is placed next to the first orange. A man now has to collect all the oranges into the basket.

He starts next to the first orange and places it in the the basket. Then goes to the second orange and brings it to the basket . Then goes to the third orange and so on. At no point does the basket move and the man is not allowed to bring more than one orange at a time.

How many meters does the man cover eventually in collecting all 50 oranges?"

Now as I worked on the solution it seemed obvious the answer was a summation of a series of numbers.

The distance he traveled to get the first orange = 0 m (The basket is next to the first orange)

The distance he traveled to get the second orange = 2m (As he has to walk to and forth to the basket each time)

The distance he traveled to get the third orange = 8m

The distance he traveled to get the fourth orange= 18m

.

.

.

so on

The total distance he traveled for collecting all 50 oranges would be 0+2+8+18+......(total of 50 terms)

This is where I got stuck. I could not properly define the series in algebraic form and I could not find a formula for summation.

Any help?

Dont feel bad.** Sometimes it is the simple questions in life which lead us to the great things**

When I was your age, even I used to ask all sots of questions in class, sometimes I would get snubbed but then other times I learnt a lot.

** Never shy away from asking for if there were no questions we would never get the answers**

**makada**- Replies: 3

Hello everyone.

I just happened to find this beautiful forum the other day while cruising on the web.

By profession I am Doctor (Pediatrician to be more specific) , but my heart belongs to mathematics ever since I was a child. I often was the odd one in my class who used to solve math problems during breaks, who used to read fat books on calculus during summer breaks . I then had a long break from maths during my med school, but now I am back again.

But now it is just for fun and to make sure my brain doesnot rust.

That is great. Thanks.

**makada**- Replies: 2

I gut stuck solving this problem. I know the answer but just cant find how to reach it. Any help?

The problem:

"Two trains start at the same time, one from London to Liverpool, the other from Liverpool to London. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?"

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