replace n with inf.
1 + (-1^0/0) = 1 +(-1^0) = 1+1= 2
lim from n toward infinity
[1+ (-1)^n/n ]
2 answers
I assume the question is asking
lim from n toward infinity (note additional parentheses):
[1+ ((-1)^n)/n ]
From the basic laws on limites, we can take this as:
Lim [1+((-1)^n/n]
= Lim 1 + Lim (-1)^n*(1/n)
= 1 + Lim (-1)^n * Lim (1/n)
= 1 + Lim (-1)^n * 0
= 1
The Lim (-1)^n is indeterminate. The upper bound is 1 and the lower bound is -1. It does not matter when it is multiplied by zero.
lim from n toward infinity (note additional parentheses):
[1+ ((-1)^n)/n ]
From the basic laws on limites, we can take this as:
Lim [1+((-1)^n/n]
= Lim 1 + Lim (-1)^n*(1/n)
= 1 + Lim (-1)^n * Lim (1/n)
= 1 + Lim (-1)^n * 0
= 1
The Lim (-1)^n is indeterminate. The upper bound is 1 and the lower bound is -1. It does not matter when it is multiplied by zero.