Determining series convergence or divergence

I tried rewriting it to 4^-n and then using the geometric series test 1/1-r
Which makes it to -1/3 convergence. I am not sure if its correct or not...

This is a geometric series. Rewrite it so the index starts at zero and (1/4)^n

I obtained a positive 1/3 when I did it.

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Originally Posted by dwsmith

I obtained a positive 1/3 when I did it.

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That probably correct can you show steps u used?

Since you have , you can rewrite it as . This is because 1 to any power is still 1.

Now, because your indexing starts at 1 instead of 0, we can subtract 1 and then add 1.

This will make the index start at 0. The adding one happens to the exponent so now we have . This can be written as .

Of course, so we just move that out side the summation.

Thus, you have a geometric series times 1/4 which is your a in the formula