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anonymous
 3 years ago
\[\lim_{x \rightarrow 1}\frac{ 2x+3x^2........+(n+1)x^n  \frac{ n(n+3) }{ 2 } }{ x1 }\]
anonymous
 3 years ago
\[\lim_{x \rightarrow 1}\frac{ 2x+3x^2........+(n+1)x^n  \frac{ n(n+3) }{ 2 } }{ x1 }\]

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what is that written ? n(n+3)/2 ?

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0did you try LH rule?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0seems legitimate to me..

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0did u get the answer ?

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1357836283297:dw

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1the derivative is \[ \frac{n x^{1+n}}{1+x}+\frac{2 x \left(1+x^n\right)}{1+x}\frac{x^2 \left(1+x^n\right)}{(1+x)^2} \]

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.0We could find the sum of this first and then apply L'Hospital's \[2x+3x^2+....(n+1)x^n\]

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1looks like we could use this formula directly http://planetmath.org/ArithmeticGeometricSeries.html

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.0\[S=2x+3x^2+...(n+1)x^n\] \[xS=2x^2+3x^3....(n+1)x^{n+1}\] \[(1x)S=2x+\underline{x^2+x^3+x^4....+x^n}(n+1)x^{n+1}\] This is GP

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1the sum would be http://www.wolframalpha.com/input/?i=differentiate+%28x^2+%28x^n1%29%2F%28x1%29%29 that's you would get indeterminate form ... you can apply L'hopital rule after that

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1you 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.

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1this is equal to http://www.wolframalpha.com/input/?i=Sum [n%28n%2B1%29%2C+{n%2C+1%2C+n}]&dataset=&equal=Submit

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0where is you confusion in this question??

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Apply Lhospital Rule...differentiate numerator and denominator with respect to variable which is x here ... dw:1358023261199:dw dw:1358023336162:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.02+ 6 + 12 ............... = n(n+1)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0my picture is not clear here.. now dw:1358023498420:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1358023535161:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1358023576877:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1358023654085:dw
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