an= 1- (0.2)^n determine whether the sequence converge or diverge , if it converges find the limit ?

Question

amistre64 · Answer

ratio test should do just fine

amistre64 · Answer

might want to take the sum of the limits tho ....

either way, a rule of thumb is for r<1; r^n goes to zero as n goes to infinity

anonymous · Answer

so is it geometric ?

amistre64 · Answer

it has a geometric feel to it, but that constant in front might mess up the definition

amistre64 · Answer

if we "drop" this down, it becomes geometric fer sure

anonymous · Answer

oh i see .. but i really need to know whats the perfect way to solve it ?

amistre64 · Answer

the limit of a sum is the sum of limits

$$\lim_{n\to~inf}~a_n$$
$$\lim_{n\to~inf}1-\lim_{n\to~inf}(0.2)^n$$
$$1-0=1$$

amistre64 · Answer

not sure how "perfect" that is ... but it suffices for simplicity

anonymous · Answer

oh now i get it ... thanks alot :)

amistre64 · Answer

good luck :)

anonymous · Answer

no its correct , because i have the final answer at back of my calculus book and its 1

anonymous · Answer

so that would be perfect ;)

anonymous · Answer

so any number to the power of infinity equals to zero??