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lgbasallote

  • 2 years ago

Prove: \[\huge S_n = \frac{n(a_n + a_1)}2\]

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  1. lgbasallote
    • 2 years ago
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    it's an easy proof....but it's still nice to see some professional do it

  2. lgbasallote
    • 2 years ago
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    i wrote that formula wrong...

  3. vishweshshrimali5
    • 2 years ago
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    See \[\S_n = \cfrac{n}{2} (2a + (n-1)d)\]

  4. lgbasallote
    • 2 years ago
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    and..?

  5. vishweshshrimali5
    • 2 years ago
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    Now put 2a +(n-1)d = a + a+(n-1)d = a_1 + a_n

  6. vishweshshrimali5
    • 2 years ago
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    You get ur answer !

  7. lgbasallote
    • 2 years ago
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    i don't think that proves anything...that was formula transformation

  8. vishweshshrimali5
    • 2 years ago
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    see a_n = a+(n-1)d

  9. vishweshshrimali5
    • 2 years ago
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    That really does //////////// :)

  10. vishweshshrimali5
    • 2 years ago
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    You don't want to use the first formula ?

  11. lgbasallote
    • 2 years ago
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    can you prove a_n = a + (n-1)d?

  12. vishweshshrimali5
    • 2 years ago
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    I think yes

  13. mathslover
    • 2 years ago
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    yep

  14. lgbasallote
    • 2 years ago
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    i think you;re confused....this is proving...not substitution

  15. shubhamsrg
    • 2 years ago
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    suppose we have 1,2,3,4.....100 adding all, we can see it like this (1+100) + (2+99) .... ( 50 + 51) => (101)*50 = (1 + 100) * (100/2) you may generalize this..

  16. vishweshshrimali5
    • 2 years ago
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    And u asked for a proof ;)

  17. lgbasallote
    • 2 years ago
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    that wasn't a proof @vishweshshrimali5 ....it was formula transformation

  18. lgbasallote
    • 2 years ago
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    and substitution isn't proving either.... @shubhamsrg

  19. vishweshshrimali5
    • 2 years ago
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    Whatever........... leave it I can prove that without using a_n formula

  20. shubhamsrg
    • 2 years ago
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    substitution ? o.O

  21. vishweshshrimali5
    • 2 years ago
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    But you will have to accept that a_n = a+(n-1)d That is basic def. of AP

  22. vishweshshrimali5
    • 2 years ago
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    I am also surprised @shubhamsrg O.o

  23. shubhamsrg
    • 2 years ago
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    i am not! ;)

  24. vishweshshrimali5
    • 2 years ago
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    ;)

  25. lgbasallote
    • 2 years ago
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    are any of you familiar with mathematical induction?

  26. vishweshshrimali5
    • 2 years ago
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    Yes

  27. vishweshshrimali5
    • 2 years ago
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    You want that proof........

  28. lgbasallote
    • 2 years ago
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    what both of you did was substitution (which is NEVER accepted as proofs)

  29. vishweshshrimali5
    • 2 years ago
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    Let P(n) be the given statement

  30. lgbasallote
    • 2 years ago
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    no. i want other proof

  31. lgbasallote
    • 2 years ago
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    induction is too dull and boring and predictable

  32. shubhamsrg
    • 2 years ago
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    you're amazing you know that ?

  33. shubhamsrg
    • 2 years ago
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    not you ! ;)

  34. vishweshshrimali5
    • 2 years ago
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    @lgbasallote please give us a "hint" of the proof u want

  35. lgbasallote
    • 2 years ago
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    actually...it's surprising @vishweshshrimali5 does know induction...

  36. shubhamsrg
    • 2 years ago
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    hint? lol..

  37. lgbasallote
    • 2 years ago
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    any proof as long as it's valid and not induction

  38. shubhamsrg
    • 2 years ago
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    induction is one of the many great tools we have in mathematics today!

  39. lgbasallote
    • 2 years ago
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    preferrably, i like to see direct proof and contradiction

  40. lgbasallote
    • 2 years ago
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    i like deduction much more

  41. vishweshshrimali5
    • 2 years ago
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    Ok lets try u want to deduce a formula from a continuous pattern

  42. lgbasallote
    • 2 years ago
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    time for the site to go down....

  43. mathslover
    • 2 years ago
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    bye

  44. vishweshshrimali5
    • 2 years ago
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    bye

  45. lgbasallote
    • 2 years ago
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    so i suppose i'll just ask this again in the fture

  46. vishweshshrimali5
    • 2 years ago
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    will check out later

  47. mathslover
    • 2 years ago
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    yep

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