Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. give the limit when the sequence converges.

{(-0.3)ⁿ}

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the sequence diverges monotonically.
b. the sequence converges monotonically. it converges to
c. the sequence converges by oscillation. it converges to
d. the sequence diverges by oscillation.

C. The sequence converges by oscillation. It converges to  0.

Step-by-step explanation:

Here as n increases magnitude of function decreases so it converges.

But at any two consecutive integers function sign changes and it oscillates. Thus it is not monotonic,

1; 35 is the ratio

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)