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Yahoo!

  • 2 years ago

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

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  1. Aryang
    • 2 years ago
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    what is that written ? n(n+3)/2 ?

  2. Aryang
    • 2 years ago
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    please confirm ?

  3. Yahoo!
    • 2 years ago
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    Yes

  4. shubhamsrg
    • 2 years ago
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    did you try LH rule?

  5. Aryang
    • 2 years ago
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    seems legitimate to me..

  6. shubhamsrg
    • 2 years ago
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    there?

  7. Yahoo!
    • 2 years ago
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    Yup..I Tried...

  8. Yahoo!
    • 2 years ago
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    n is Constant Ryt ?

  9. ash2326
    • 2 years ago
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    Yes n is constant

  10. AravindG
    • 2 years ago
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    did u get the answer ?

  11. Yahoo!
    • 2 years ago
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    Nope

  12. experimentX
    • 2 years ago
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    |dw:1357836283297:dw|

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

  15. experimentX
    • 2 years ago
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    looks like we could use this formula directly http://planetmath.org/ArithmeticGeometricSeries.html

  16. ash2326
    • 2 years ago
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    \[S=2x+3x^2+...(n+1)x^n\] \[xS=2x^2+3x^3....(n+1)x^{n+1}\] \[(1-x)S=2x+\underline{x^2+x^3+x^4....+x^n}-(n+1)x^{n+1}\] This is GP

  17. experimentX
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    where is you confusion in this question??

  21. Taufique
    • 2 years ago
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    Apply L-hospital Rule...differentiate numerator and denominator with respect to variable which is x here ... |dw:1358023261199:dw| |dw:1358023336162:dw|

  22. Yahoo!
    • 2 years ago
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    2+ 6 + 12 ............... = n(n+1)

  23. Taufique
    • 2 years ago
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    my picture is not clear here.. now |dw:1358023498420:dw|

  24. Taufique
    • 2 years ago
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    |dw:1358023535161:dw|

  25. Taufique
    • 2 years ago
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    |dw:1358023576877:dw|

  26. Taufique
    • 2 years ago
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    |dw:1358023654085:dw|

  27. Yahoo!
    • 2 years ago
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    got it..:)

  28. Taufique
    • 2 years ago
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    solve it..and find L

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