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lgbasallote

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

  • one year ago
  • one year ago

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

    • one year ago
  2. lgbasallote
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    i wrote that formula wrong...

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

    • one year ago
  4. lgbasallote
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    and..?

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

    • one year ago
  6. vishweshshrimali5
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    You get ur answer !

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

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

    • one year ago
  9. vishweshshrimali5
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    That really does //////////// :)

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

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

    • one year ago
  12. vishweshshrimali5
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    I think yes

    • one year ago
  13. mathslover
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    yep

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

    • one year ago
  15. shubhamsrg
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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..

    • one year ago
  16. vishweshshrimali5
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    And u asked for a proof ;)

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

    • one year ago
  18. lgbasallote
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    and substitution isn't proving either.... @shubhamsrg

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

    • one year ago
  20. shubhamsrg
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    substitution ? o.O

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

    • one year ago
  22. vishweshshrimali5
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    I am also surprised @shubhamsrg O.o

    • one year ago
  23. shubhamsrg
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    i am not! ;)

    • one year ago
  24. vishweshshrimali5
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    ;)

    • one year ago
  25. lgbasallote
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    are any of you familiar with mathematical induction?

    • one year ago
  26. vishweshshrimali5
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    Yes

    • one year ago
  27. vishweshshrimali5
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    You want that proof........

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

    • one year ago
  29. vishweshshrimali5
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    Let P(n) be the given statement

    • one year ago
  30. lgbasallote
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    no. i want other proof

    • one year ago
  31. lgbasallote
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    induction is too dull and boring and predictable

    • one year ago
  32. shubhamsrg
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    you're amazing you know that ?

    • one year ago
  33. shubhamsrg
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    not you ! ;)

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

    • one year ago
  35. lgbasallote
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    actually...it's surprising @vishweshshrimali5 does know induction...

    • one year ago
  36. shubhamsrg
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    hint? lol..

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

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

    • one year ago
  39. lgbasallote
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    preferrably, i like to see direct proof and contradiction

    • one year ago
  40. lgbasallote
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    i like deduction much more

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

    • one year ago
  42. lgbasallote
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    time for the site to go down....

    • one year ago
  43. mathslover
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    bye

    • one year ago
  44. vishweshshrimali5
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    bye

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

    • one year ago
  46. vishweshshrimali5
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    will check out later

    • one year ago
  47. mathslover
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    yep

    • one year ago
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