Question

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

Answer 1

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

Answer 2

i tried but i only reemplace X?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

of course you can

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

got it clauixx?

Answer 13

yes :D thanks :D:D