Question

\[ 1/\sqrt{2} -1/\sqrt{3} + 1/\sqrt{4} -1/\sqrt{5} + 1/\sqrt{6} - \] ....

I'm not sure if my series below is written correctly

\[\sum_{n=2}^{infty} (-1)^{n-1}/\sqrt{n}\]

Answer 1

now I have to determine if it's convergent
lets see...

Answer 2

(-1)^n

Answer 3

here is what bothers me about these equations...an "n" as an exponent and the other one just in the denominator....i would use the p-series test if it wasn't for the numerator

Answer 4

it's convergent because 1/sq(n) decreasing and approach to zero.
so libnitz test said (-1)^n/sq(n) series is convergent.

Answer 5

(-1)^n...oh lol

Answer 6

ok ...remind me of libniz test...sorry for the bother

Answer 7

(-1)^n=1,-1,1,-1,1,-1,,,,,

Answer 8

suppose an is a decreasing sequences and approaching to zero so sigma of (-1)^n*an is a convergence series.That's it !

Answer 9

ok

Answer 10

another question...just because it's a leibniz alternating series it's automatically convergent?

Answer 11

http://www.math24.net/alternating-series.html

definition of alternating series