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

Question

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

anonymous · Answer

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

anonymous · Answer

i tried but i only reemplace X?

anonymous · Answer

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

anonymous · Answer

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

a_clan · Answer

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

anonymous · Answer

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

a_clan · Answer

of course you can

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

got it clauixx?

anonymous · Answer

yes :D thanks :D:D