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

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AryangBest ResponseYou've already chosen the best response.0
what is that written ? n(n+3)/2 ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
did you try LH rule?
 one year ago

AryangBest ResponseYou've already chosen the best response.0
seems legitimate to me..
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
did u get the answer ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1357836283297:dw
 one year ago

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

ash2326Best ResponseYou've already chosen the best response.0
We could find the sum of this first and then apply L'Hospital's \[2x+3x^2+....(n+1)x^n\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like we could use this formula directly http://planetmath.org/ArithmeticGeometricSeries.html
 one year ago

ash2326Best 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.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.
 one year ago

experimentXBest ResponseYou've already chosen the best response.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
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
where is you confusion in this question??
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
Apply Lhospital Rule...differentiate numerator and denominator with respect to variable which is x here ... dw:1358023261199:dw dw:1358023336162:dw
 one year ago

Yahoo!Best ResponseYou've already chosen the best response.0
2+ 6 + 12 ............... = n(n+1)
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
my picture is not clear here.. now dw:1358023498420:dw
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
dw:1358023535161:dw
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
dw:1358023576877:dw
 one year ago

TaufiqueBest ResponseYou've already chosen the best response.1
dw:1358023654085:dw
 one year ago
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