- #1
alovesong
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Homework Statement
Determine whether or not the sequences below are summable:
{(-1)^n}
{(-1)^n + (-1)^(n+1)}
{(-1)^n} + {(-1)^(n+1)}
Homework Equations
The Attempt at a Solution
Okay, I'm having some trouble thinking about these the right way. Since
{(-1)^n}= -1, 1, -1, 1, ... then its sum = -1, 0, -1, 0, -1.
I think this means that it is not summable even though it is 0 every other term.
Assuming it is divergent, then {(-1)^(n+1)} is of course also divergent... But I think that two divergent sequences added together might be convergent.
But does it matter whether they are summed together as one sequence or two? Either way they will still = 0, 0, 0, 0, 0 ... right? So would they both be summable? Sorry if I sound confused - it's just because I am.