Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby japiga on Mon Sep 20, 2010 3:42 pm

Please may s.o. to help me to solve the sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000.
japiga
 
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm

Sponsor

Sponsor
 

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby maggiemagnet on Tue Sep 21, 2010 12:02 am

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?
User avatar
maggiemagnet
 
Posts: 287
Joined: Mon Dec 08, 2008 12:32 am

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby japiga on Tue Sep 21, 2010 8:03 am

geometric progression?
japiga
 
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby japiga on Tue Sep 21, 2010 8:04 am

But how to put it in mathematic formula? I have no idie at this moment.
japiga
 
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby maggiemagnet on Tue Sep 21, 2010 10:54 am

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? :thumb:
User avatar
maggiemagnet
 
Posts: 287
Joined: Mon Dec 08, 2008 12:32 am

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby Martingale on Wed Sep 22, 2010 11:38 am

use...



and




your sum...

User avatar
Martingale
 
Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby japiga on Wed Sep 22, 2010 1:22 pm

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!
japiga
 
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby Martingale on Wed Sep 22, 2010 1:26 pm

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
User avatar
Martingale
 
Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby japiga on Wed Sep 22, 2010 1:49 pm

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?
japiga
 
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm

Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Postby Martingale on Wed Sep 22, 2010 1:54 pm

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
User avatar
Martingale
 
Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

Next

Return to Advanced Algebra ("pre-calculus")

cron