Question

is this series alternating ?
sigma n=1 to infinity (-1)^n(2-1/n).

Answer 1

I don't think so, I think it's possible to have consecutive negative terms

Answer 2

the answer is that its is but it doesnt satisfy the conditions

Answer 3

2-1/n is always positive for n>=1 so it is an alternating series.
lim n->inf 2-1/n = 2 so it diverges by the alternating series test.

Answer 4

If you plug in the n values, you're going to get imaginary numbers.. maybe every number that is real ends up alternating?

Answer 5

Not that I found any.. lol

Answer 6

i think he means (-1)^n * [2-1/n], and even if it were (-1)^(n*[2-1/n] then the terms approach (-1)^(2n) = 1, essentially equivalent to summing an infinite number of 1's, therefore, irrelevant of whether it exists in the complex plane, it diverges.

Answer 7

Oh, then it's alternating for sure. (-1)^n would change the sign each time