Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Yahoo!

  • one year ago

\[\lim_{x \rightarrow 1}\frac{ 2x+3x^2........+(n+1)x^n - \frac{ n(n+3) }{ 2 } }{ x-1 }\]

  • This Question is Closed
  1. Aryang
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is that written ? n(n+3)/2 ?

  2. Aryang
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    please confirm ?

  3. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

  4. shubhamsrg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    did you try LH rule?

  5. Aryang
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    seems legitimate to me..

  6. shubhamsrg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there?

  7. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yup..I Tried...

  8. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    n is Constant Ryt ?

  9. ash2326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes n is constant

  10. AravindG
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    did u get the answer ?

  11. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope

  12. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1357836283297:dw|

  13. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the derivative is \[ \frac{n x^{1+n}}{-1+x}+\frac{2 x \left(-1+x^n\right)}{-1+x}-\frac{x^2 \left(-1+x^n\right)}{(-1+x)^2} \]

  14. ash2326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We could find the sum of this first and then apply L'Hospital's \[2x+3x^2+....(n+1)x^n\]

  15. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    looks like we could use this formula directly http://planetmath.org/ArithmeticGeometricSeries.html

  16. ash2326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[S=2x+3x^2+...(n+1)x^n\] \[xS=2x^2+3x^3....(n+1)x^{n+1}\] \[(1-x)S=2x+\underline{x^2+x^3+x^4....+x^n}-(n+1)x^{n+1}\] This is GP

  17. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the sum would be http://www.wolframalpha.com/input/?i=differentiate+%28x^2+%28x^n-1%29%2F%28x-1%29%29 that's you would get indeterminate form ... you can apply L'hopital rule after that

  18. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you should be getting \[ \frac{1}{3} n \left(2+3 n+n^2\right) \] or since you know you get indeterminate form ... you could apply L'hopital rule from the start. that's way easier.

  19. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this is equal to http://www.wolframalpha.com/input/?i=Sum[n%28n%2B1%29%2C+{n%2C+1%2C+n}]&dataset=&equal=Submit

  20. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where is you confusion in this question??

  21. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Apply L-hospital Rule...differentiate numerator and denominator with respect to variable which is x here ... |dw:1358023261199:dw| |dw:1358023336162:dw|

  22. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2+ 6 + 12 ............... = n(n+1)

  23. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    my picture is not clear here.. now |dw:1358023498420:dw|

  24. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1358023535161:dw|

  25. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1358023576877:dw|

  26. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1358023654085:dw|

  27. Yahoo!
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got it..:)

  28. Taufique
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    solve it..and find L

  29. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.