Please may s.o. to help me to solve the sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000.

- maggiemagnet
**Posts:**350**Joined:**Mon Dec 08, 2008 12:32 am-
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japiga wrote:Please may s.o. to help me to solve the sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000.

These products are what is called "rectangular" numbers because, if you draw the products in "dot" form, you get rectangles. For instance:

Code: Select all

`2: **`

6: ***

***

12: ****

****

****

What have you found when you've tried to find a pattern? For instance:

2 = 2

2 + 6 = 8

2 + 6 + 12 = 20

2 + 6 + 12 + 20 = 40

2 + 6 + 12 + 20 + 30 = 70

Where did this lead you?

geometric progression?

But how to put it in mathematic formula? I have no idie at this moment.

- maggiemagnet
**Posts:**350**Joined:**Mon Dec 08, 2008 12:32 am-
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japiga wrote:geometric progression?

To be a geometric series, there would have to be a common ratio. Is there?

What did you find at the link in my previous post?

- Martingale
**Posts:**335**Joined:**Mon Mar 30, 2009 1:30 pm**Location:**USA-
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Dear Martingale. T hose sums are not sums of orders: geometric and arithmetic sum of order. Please give me more details it is very important to me. How to calculate sum of i^2 = 1^2+2^2+3^2…..+ 999^2 and sum of i = 1 + 2 +3 + …. + 999. Hot to calculate it? I have to know exact sum number. It is huge number of ciphers!!? Please help me!

- Martingale
**Posts:**335**Joined:**Mon Mar 30, 2009 1:30 pm**Location:**USA-
**Contact:**

japiga wrote:Dear Martingale. T hose sums are not sums of orders: geometric and arithmetic sum of order. Please give me more details it is very important to me. How to calculate sum of i^2 = 1^2+2^2+3^2…..+ 999^2 and sum of i = 1 + 2 +3 + …. + 999. Hot to calculate it? I have to know exact sum number. It is huge number of ciphers!!? Please help me!

I gave you the formulas for the sum of and

Just plug 999 into the formulas

the first one is clear, it is arithmetic order: 1 + 2 + 3 + ... + 999, since d = 1 and it is easy to calculate, but what is with another one 1^2+2^2+3^2…..+ 999^2. It is not geometric progression order. How to calculate this one?

- Martingale
**Posts:**335**Joined:**Mon Mar 30, 2009 1:30 pm**Location:**USA-
**Contact:**

japiga wrote:the first one is clear, it is arithmetic order: 1 + 2 + 3 + ... + 999, since d = 1 and it is easy to calculate, but what is with another one 1^2+2^2+3^2…..+ 999^2. It is not geometric progression order. How to calculate this one?

Like I have above...

your