00:01
In this question, we want to determine whether the sequence converges or diverges, and if it converges, we're going to find the limit.
00:07
Here, my a sub n is equal to the quantity of 7n over n plus 1 being raised to the n power.
00:15
So here, what we're looking at is the limit as n approaches infinity of the quantity of 7n over n plus 1 raised to the n power, and we're going to work from the inside out this time.
00:33
In other words, first, i'm going to ask myself, what is the limit as n approaches infinity of 7n over n plus 1? i notice i have a rational function, a polynomial over a polynomial.
00:48
I also notice that the degree of the numerator is the same as the degree of the denominator, namely, the degrees of the top and bottom are both just 1.
00:58
So to find the limit of this rational function as n approaches infinity, i just take my ratio of the leading coefficients, 7 over 1, which is 7.
01:11
And so as n approaches infinity, what's inside these parentheses is approaching 7, while my exponent, that's approaching infinity.
01:25
So essentially here, i have 7 being raised to the infinity power...