Question

LEIBNIZ TEST!

Answer 1

why can't it be applied to..... 1/2 - 1/3 + 1/2^2 - 1/3^2 + 1/2^3 - 1/3^3... what method can be used to show convergence?

Answer 2

Is the absolute value sequence decreasing?

Answer 3

ummmmmmm. . . maybe? lol

Answer 4

That sequence definitely looks like a zero-sequence to me, so the Leibniz-test can be applied. The series converges!

Answer 5

yep

Answer 6

um..it says it cannot be applied. and I have to explain why not.

Answer 7

It probably seems convergent because I don't know how to use the division sign on here :/

Answer 8

Between 1/2^n and 1/2^(n+1) you have 1/3^n. But now
1/2^n > 1/3^n < 1/2^(n+1)
So the absolute value sequence is not decreasing, hence we can't apply the Leibniz's test!