Could anyone please tell me how do we change the order of summation?

Hi... Could anyone give me a logical explanation on how to change the order of summation as used in the problem: https://brilliant.org/discussions/thread/sequences-problem/ ?

Pls use examples of maybe any other series which uses the same concept..

Thanks in advance..

#HelpMe! #MathProblem #Math

Easy Math Editor

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`2^{34}`	$2^{34}$
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Comments

Let's say we want to add 1+4+9+16+25...225.

$\sum^15_{r=1} r^2$

Now we break the squares apart: 1+(1+3)+(1+3+5)+(1+3+5+7)+(1+3+...+9)...+(1+3+...29)

$\sum^15_{r=1} \sum^r_{m=1} 2m-1$

Now we rearrange everything: $1 \times 15+3 \times 14+5 \times 13.....29 \times 1$

$\sum^15_{r=1} (2r-1)(16-r)$

Well, I hope this answers that.

Clarence Chew - 8 years, 1 month ago

can i

InoxcEnt Haris - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$