Which statement is true about the series the summation from n equals 1 to infinity of 3 plus 2 times the quantity k minus 1 ?

Question

Which statement is true about the series  ?

A	It converges to 0.
B	It is arithmetic.
C	It converges to some unknown value.
D	It is geometric.

Answer 1

You get the first term by plugging in n = 1 according to the summation. but notice that there is no "n" in the expression so the first term is just "3 + 2(k - 1)" which is 3 + 2k - 2 which is 1 + 2k.

The second term is the same (because there is no "n" to index. So the second term is also 1 + 2k making the sum now (1 + 2k) + (1 + 2k) = 2 + 4k so a summary would be:

I added an example column for reference. Try your own value of "k" to convince yourself that it doesn't matter what "k" is, the relationship still exists.

So obviously, it does not converge. And you can see it is arithmetic.