can anyone tell me ..

an= e^n is diverging and an= 1/e^n is converging ...

yes or no

i said yes

plz confrom

Yes, you are correct. The sequence given as an = e^n is diverging, while the sequence an = 1/e^n is converging.

To understand why, let's look at the definition of convergence and divergence of sequences.

A sequence is said to be converging if its values approach a finite limit as n approaches infinity. In other words, as n gets larger and larger, the terms of the sequence get closer and closer to a specific value. On the other hand, a sequence is said to be diverging if its values do not approach a finite limit as n goes to infinity. In this case, the terms of the sequence either keep growing indefinitely or keep oscillating without settling down to a particular value.

For the sequence an = e^n, as n approaches infinity, the values of e^n grow exponentially. The exponential function e^n increases rapidly as n increases, and there is no finite limit that the terms of this sequence approach. Hence, it is diverging.

On the other hand, for the sequence an = 1/e^n, as n approaches infinity, the values of 1/e^n tend towards zero. The exponential function e^n increases at a faster rate than n, so the denominator e^n grows faster than the numerator 1. As a result, the terms of this sequence approach zero as n increases, indicating convergence towards zero.

Therefore, an = e^n is diverging, and an = 1/e^n is converging.