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anonymous

  • 5 years ago

prove the statement true : 1^2 +4^2 + 7^2 + ..... + (3n-2)^2 = [n (6n^2 - 3n -1)] / 2

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  1. myininaya
    • 5 years ago
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    did you see my earlier reply to this?

  2. anonymous
    • 5 years ago
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    i dont see it :(

  3. myininaya
    • 5 years ago
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    oh wait nvm ignore the early one do you know anything about induction?

  4. anonymous
    • 5 years ago
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    some1 tell me put n=1 and see both side equal , then that's proved

  5. anonymous
    • 5 years ago
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    but when i try another n=2 then it s not equal

  6. myininaya
    • 5 years ago
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    for n=1 we have (3*1-2)^2=1^2=1 on lhs we have 1*(6*1^2-3*1-1)/2=2/2=1 on rhs so now we get to assume is true for k>=1 and now we have to show it is true for k+1

  7. myininaya
    • 5 years ago
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    1^2+4^2+7^2+....+(3k-2)^2+(3(k+1)-2)^2 we want to show this equals the other side (whereever this is n we need k+1 to be there)

  8. myininaya
    • 5 years ago
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    so we know 1^2+4^2+...+(3k-2)^2=k(6k^2-3k-1)/2 so we have k[6k^2-3k-1]/2+(3(k+1)-2)^2 we need to manipulate this so that it is (k+1)*(6(k+1)^2-3(k+1)-1)/2 ok? try to do this

  9. myininaya
    • 5 years ago
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    oh hello, n=2 it does work for n=2 we have on lhs 1^2+4^2=1+16=17 on rhs we have 2(6*2^2-3*2-1)/2=24-6-1=17 so does work for n=2

  10. anonymous
    • 5 years ago
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    it wont work for the k+1 because the LHS ^ 2 and the RHS ^ 3 ? So can you explain more about this ? :-<

  11. myininaya
    • 5 years ago
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    ?

  12. myininaya
    • 5 years ago
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    what do you mean?

  13. anonymous
    • 5 years ago
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    let me try this again

  14. myininaya
    • 5 years ago
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    here i will scan what i did. you really have to know some algbra for this

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  15. myininaya
    • 5 years ago
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    i added in alot of zeroes i forced it to be what i want and then the left overs canceled with the other left overs :)

  16. myininaya
    • 5 years ago
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    do you have any questions?

  17. anonymous
    • 5 years ago
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    i got it now really appreciate for your help

  18. myininaya
    • 5 years ago
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    so you actually understood all the weird stuff i did? lol

  19. anonymous
    • 5 years ago
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    no i did it another way and got the answer

  20. myininaya
    • 5 years ago
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    if i looked back on this, i would be like wtf

  21. anonymous
    • 5 years ago
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    LOLLLLL

  22. myininaya
    • 5 years ago
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    lol i was trying to do it another way and i kept failing

  23. myininaya
    • 5 years ago
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    can you post what you did

  24. anonymous
    • 5 years ago
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    i dont know how to post the paper attaach in here , and i dont have the scan machine :(

  25. anonymous
    • 5 years ago
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    but i will try to type it then

  26. myininaya
    • 5 years ago
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    no worries lol

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