Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
Please may s.o. to help me to solve the sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000.
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maggiemagnet
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Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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?
Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
geometric progression?
Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
But how to put it in mathematic formula? I have no idie at this moment.
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maggiemagnet
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Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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?
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Martingale
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Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
use...
}{2})
and
(2n+1)}{6})
your sum...
=\sum_{i=1}^{999}(i^2+i)=\sum_{i=1}^{999}i^2+\sum_{i=1}^{999}i=\cdots)
and
your sum...
Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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!
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Martingale
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Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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
Just plug 999 into the formulas
Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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?
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Martingale
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Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000
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