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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

did you try LH rule?
seems legitimate to me..
there?
Yup..I Tried...
n is Constant Ryt ?
Yes n is constant
did u get the answer ?
Nope
|dw:1357836283297:dw|
the derivative is \[ \frac{n x^{1+n}}{-1+x}+\frac{2 x \left(-1+x^n\right)}{-1+x}-\frac{x^2 \left(-1+x^n\right)}{(-1+x)^2} \]
We could find the sum of this first and then apply L'Hospital's \[2x+3x^2+....(n+1)x^n\]
looks like we could use this formula directly http://planetmath.org/ArithmeticGeometricSeries.html
\[S=2x+3x^2+...(n+1)x^n\] \[xS=2x^2+3x^3....(n+1)x^{n+1}\] \[(1-x)S=2x+\underline{x^2+x^3+x^4....+x^n}-(n+1)x^{n+1}\] This is GP
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
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.
this is equal to http://www.wolframalpha.com/input/?i=Sum[n%28n%2B1%29%2C+{n%2C+1%2C+n}]&dataset=&equal=Submit
where is you confusion in this question??
Apply L-hospital Rule...differentiate numerator and denominator with respect to variable which is x here ... |dw:1358023261199:dw| |dw:1358023336162:dw|
2+ 6 + 12 ............... = n(n+1)
my picture is not clear here.. now |dw:1358023498420:dw|
|dw:1358023535161:dw|
|dw:1358023576877:dw|
|dw:1358023654085:dw|
got it..:)
solve it..and find L

Not the answer you are looking for?

Search for more explanations.

Ask your own question