Question

1 Identify whether the series summation of 16 open parentheses 5 close parentheses to the I minus 1 power from 1 to infinity is a convergent or divergent geometric series and find the sum, if possible.

A This is a convergent geometric series. The sum cannot be found. (I think this)

B This is a divergent geometric series. The sum cannot be found.

C This is a convergent geometric series. The sum is –4.

D This is a divergent geometric series. The sum is –4.

Answer 1

you can pull out constants ...

Answer 2

pull out 16/5

does 5^i converge?

Answer 3

To be honest, Amistre, I don't know. I don't understand convergents and disconvergents so I looked it up and this is the formula for convergent and it can't be solved

Answer 4

if we do a ratio setup for convergence:

\[\lim\frac{16(5)^{i+1-1}}{16(5)^{i-1}}\]
\[\lim16(5)=80\]
if this converges then:

80 < 1 is true

Answer 5

if it converges ... then you can find a number that it cannot bypass.

\[\frac{16}{5}(5+5^2+5^3+5^4+...)\]
\[16(1+5+5^2+5^3+5^4+...)\]
does this seem to converge ... to level out .. to calculate to some difinte value?

Answer 6

so is my answer right?


i dont know

Answer 7

convergent would indicate that a sum can be found ...

Answer 8

something cannot be convergent and have no discernable value.

Answer 9

if you keep growing by 3 inches each year, how tall till you eventually get?

Answer 10

oh.. so it's disconvergent? when i looked it up, the disconvergent formula had a fraction in it .-.

Answer 11

its divergent :) and since its divergent, a sum cannot be found.

Answer 12

Ty!!! this was correct!!