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Math help needed !

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So, I'm having a problem with question 39 of this picture.

As other picture shows I've managed to prove that i^3 indeed equals area of L-shaped region, (don't get confused by that I used d not i, i looked too much like 1) but how should I proceed to verify formula for sums of cubes.

Any help apprechiated ! :)

-Emilia

post-142736-0-28195200-1431177462_thumb.

post-142736-0-36374600-1431177488_thumb.

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So, I'm having a problem with question 39 of this picture.

As other picture shows I've managed to prove that i^3 indeed equals area of L-shaped region, (don't get confused by that I used d not i, i looked too much like 1) but how should I proceed to verify formula for sums of cubes.

Any help apprechiated ! :)

-Emilia

 

You seem to have done most of the work already. The expression that you've derived (i^3) is essentially the area of the ith L-shaped region. So the sum of the cubes is basically the sum of the areas of all the L-shaped regions. And since the sum of all the L-shaped regions is simply the area of the big square, thus the sum of the cubes is the area of the big square :)

 

Mathematically:

gif.latex? \sum_{i=1}^{n} i^3 = \sum_{i=

 

gif.latex? = \left(\frac{n(n+1)}{2}\righ

 

Looks much fancier with the mathematical formulae, doesn't it? :P :P :P

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Thank you !

So, I'm having a problem with question 39 of this picture.

As other picture shows I've managed to prove that i^3 indeed equals area of L-shaped region, (don't get confused by that I used d not i, i looked too much like 1) but how should I proceed to verify formula for sums of cubes.

Any help apprechiated ! :)

-Emilia

 

You seem to have done most of the work already. The expression that you've derived (i^3) is essentially the area of the ith L-shaped region. So the sum of the cubes is basically the sum of the areas of all the L-shaped regions. And since the sum of all the L-shaped regions is simply the area of the big square, thus the sum of the cubes is the area of the big square :)

 

Mathematically:

gif.latex? \sum_{i=1}^{n} i^3 = \sum_{i=

 

gif.latex? = \left(\frac{n(n+1)}{2}\righ

 

Looks much fancier with the mathematical formulae, doesn't it? :P :P :P

Ahhh! I feel so dumb atm :D

Thanks for writing it with "language of math", verbal instructions are what ruin me. Now its clear :)

Btw, how did you manage to put that calculation into your message that way?

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Thank you !

 

So, I'm having a problem with question 39 of this picture.

As other picture shows I've managed to prove that i^3 indeed equals area of L-shaped region, (don't get confused by that I used d not i, i looked too much like 1) but how should I proceed to verify formula for sums of cubes.

Any help apprechiated ! :)

-Emilia

 

You seem to have done most of the work already. The expression that you've derived (i^3) is essentially the area of the ith L-shaped region. So the sum of the cubes is basically the sum of the areas of all the L-shaped regions. And since the sum of all the L-shaped regions is simply the area of the big square, thus the sum of the cubes is the area of the big square :)

 

Mathematically:

gif.latex? \sum_{i=1}^{n} i^3 = \sum_{i=

 

gif.latex? = \left(\frac{n(n+1)}{2}\righ

 

Looks much fancier with the mathematical formulae, doesn't it? :P :P :P

Ahhh! I feel so dumb atm :D

Thanks for writing it with "language of math", verbal instructions are what ruin me. Now its clear :)

Btw, how did you manage to put that calculation into your message that way?

 

 

I use the LaTex code to write those symbols. You can take a look at Sandwich's post here: http://www.ibsurvival.com/topic/15583-quick-guide-to-maths-symbols-on-the-computer/

LaTex is fairly intuitive and easy to use. For example, let's say that you want to type the Greek letter "omega", all you need to type is: \omega. For more complicated symbols, you can just search on google for how to type them in LaTex.

Btw, you can see how I typed those symbols above by trying to quote my post. Because when you put those formulae in IBS text editor, they will be displayed as plain text :)

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