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Proof by Induction Question

is the (summation of r) all squared the same as summation of r ^2
or how can i write it
(edited 9 years ago)
Original post by bigmindedone
is the (summation of r) all squared the same as summation of r ^2
or how can i write it


No. 5=12+22(1+2)2=32=95 = 1^2 + 2^2 \neq (1+2)^2 = 3^2 = 9
Original post by bigmindedone
is the (summation of r) all squared the same as summation of r ^2
or how can i write it


Try it from terms 1 to 5. You'll see the values are different.
how can i summarize it like i know for r ^2 it is but the other i dont know
Reply 4
Original post by bigmindedone
is the (summation of r) all squared the same as summation of r ^2
or how can i write it

No e.g.

Unparseable latex formula:

\displaystyle \left(\sum_{r=1}^{2} r\right)^2 = \left(1+2)^2 = 9



r=12r2=12+22=5\displaystyle \sum_{r=1}^{2} r^2 = 1^2+2^2 = 5

It's similar to the notion that (x+y)2≢x2+y2(x+y)^2\not\equiv x^2+y^2.
Do you have the actual question?
Original post by Slowbro93
Do you have the actual question?



But i just wanna know what i can change the second part to to make the proof easier to find
Its a proof by induction
(edited 9 years ago)
Original post by bigmindedone



But i just wanna know what i can change the second part to to make the proof easier to find
Its a proof by induction


Can you show us what you've done so far? You may be overcomplicating it for yourself
Reply 8
Original post by bigmindedone



But i just wanna know what i can change the second part to to make the proof easier to find
Its a proof by induction


I think the answer you're looking for is n(n+1)/2. Have you not seen this result before?

(you should be familiar with it as the sum of an AP!)

EDIT: and you need to square that result, obviously :smile:
Ah yes thanks just square it im overthinking it

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