Question

Consider the infinite geometric series

∑
∞
n
=
1
−
4
(
1
3
)
n
−
1
. In this image, the lower limit of the summation notation is "n = 1".

a. Write the first four terms of the series.
b. Does the series diverge or converge?
c. If the series has a sum, find the sum
please show all steps

Answer 1

[AI-generated answer — Bot]

a. The first four terms of the series are: -4/3, 4/9, -16/27, 64/81.

b. The series converges.

c. The sum of the series is S = -4/3 + 4/9 - 16/27 + 64/81 + ... = -4/3(1 + 1/3 + 1/9 + 1/27 + ...). Using the formula for the sum of a geometric series, S = -4/3(1/(1 - 1/3)) = -4/3(3/2) = -2.

Answer 2

No idea what that column of symbols is. Type it in a normal way