Question

can someone help me with the limits?

Answer 1

sure

Answer 2

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

Answer 3

and show full solution if u can

Answer 4

It's possible to use L'Hopital's Rule here, since both the numerator and the denominator go to zero at x -> 1.
\[\lim_{x \rightarrow 1}\frac{f(x)}{g(x)}=\lim_{x \rightarrow 1}\frac{f'(x)}{g'(x)}\]So firstly, what do you get when you differentiate the numerator with respect to x?

Secondly, what do you get when you differentiate the denominator with respect to x?

Answer 5

i think of lhopitals rule
take derivative from nominator and denominator to get :

(1 +2x + 3x^2 + 4x^3 + ... + nx^(n-1)) / 1

Answer 6

thanks but its not the way i look at it. its the geometrical sequence, so i should use the sequence's sum formula...