Question

plz solve this:
limit [(-1)^n+1]/2n-1
n->infinity

Answer 1

0

Answer 2

Notice that
\[\left| \frac{(-1)^n-1}{2n-1} \right| \leq \left| \frac{2}{2n-1} \right| \leq \left| \frac{2}{2n} \right| = \frac{1}{n}\]

Answer 3

Now the limit as n --> infty of 1/n = 0. Hence the limit of your thing as n --> infty is also 0.

Answer 4

it becomes too tough 4 me
can u tel me an easy method of solving this

Answer 5

I should have written +1 in my first term, but it doesn't change anything afterwards.

Answer 6

the numerator can only yield values of ±1 no matter what n is
the denominator is increasing as n increases therefore the fraction will decrease with n

pushing to the limit as n approaches infinity high numbers can only make the expression approach zero

Answer 7

(unless the +1 is not in the index in which case the numerator can only yield 0 or 2)

Answer 8

it becomes too tough 4 me
can u tel me an easy method of solving this

Answer 9

tell ne what is Lt (-1)^n+1
n->infty

Answer 10

is that Lt (-1)^(n+1)
n->infty

or Lt ((-1)^n)+1)
n->infty

Answer 11

plz tell me by solving not only by giving ans directly

Answer 12

it is (-1)^(n+1)

Answer 13

This is a graph of f(n) = (-1)^(n+1)