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proof

Question
Show that the sum of the first n odd numbers is a perfect square
hence show that 57^{2} - 13^{2} [\latex] is the sum of certain consecutive odd numbers and find them


my working is attached

please point out of i got any thing wrong


thank you Scan0022.jpg
Attachment not found
Scan0023.jpg320.5KB
Original post by bigmansouf
Question
Show that the sum of the first n odd numbers is a perfect square
hence show that 57^{2} - 13^{2} [\latex] is the sum of certain consecutive odd numbers and find them


my working is attached

please point out of i got any thing wrong


thank you Scan0022.jpg
Attachment not found


I think you may have misunderstood the question. 'first n odd numbers' for the first part (eg 1+3+5=9) and not necessarily 2 consecutive odd numbers for the second. Try again, and I'll try my best to help after that.

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Reply 2
Avatar for Buses
Buses
9
DSC_1509.jpg this is a very quick and simple proof. Here is the first part...the second part actually flows quite nicely but i'll leave you spot the trick

Use first part to help with second
(edited 8 years ago)
Original post by Buses
...


I don't think an answer is necessary atm, given that OP has yet to actually try the question being asked.

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Original post by Renzhi10122
I don't think an answer is necessary atm, given that OP has yet to actually try the question being asked. But good proof, I hadn't actually come across that method.

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Original post by Renzhi10122


What was your way. I just did it the straight forward way.


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Original post by physicsmaths
What was your way. I just did it the straight forward way.


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Induction

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Reply 7
Avatar for Timianey
Timianey
I have proving of Integration for Tan X , Cot X, Cosec X and Sec X here at http://alevelfurthermaths.blogspot.com/2015/07/revision-guide-integrals-proving.html . I lost all the photos but i managed to post it before at my blog . I hope it helps :smile:
Reply 8
Avatar for mSayed
mSayed
1
Here's another way to prove it..

daum_equation_1438140708284.png
Reply 9
Avatar for bigmansouf
bigmansouf
OP
20
Original post by mSayed
Here's another way to prove it..

daum_equation_1438140708284.png


thanks
Arguably the most illuminating proof:

Spoiler



(oops - didn't realise the image was quite this big when I linked it!).

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