Mathematics 35 Online
OpenStudy (anonymous):

What is the limit in this example? Lim (x+x^2+x^3+....+x^n-n)/(x-1) When X->1 ???

OpenStudy (anonymous):

Try rewriting the numerator as (x-1) + (x^2-1) + ... + (x^n - 1).

OpenStudy (anonymous):

i tried but i only reemplace X?

OpenStudy (anonymous):

i cant add -1 unless i add +1 :S because u cant add numbers like that or not?

OpenStudy (anonymous):

There is a -n at the end, you are just splitting that into n -1s.

OpenStudy (a_clan):

take (x-1) out as common in numerator and cancel from denominator

OpenStudy (anonymous):

i can do that? i mean i tried but my friend said that i cant do that

OpenStudy (a_clan):

of course you can

OpenStudy (anonymous):

$\frac {x^k - 1} {x-1} = (1 + x + ... + x^{k-1} )$

OpenStudy (anonymous):

$(x-1)/(x-1)+(x^2-1)/(x-1)+(x^3-1)/(x-1)+...+(x^n-1)/(x-1)$ Then apply the limit...

OpenStudy (anonymous):

x^k?? shouldn't that be x? so i can cancel it?

OpenStudy (anonymous):

which will come as 1+2+3+...+n

OpenStudy (anonymous):

got it clauixx?

OpenStudy (anonymous):

yes :D thanks :D:D