Question

An infinite Series Sn has partial sum formula Pn = (2n+1)/(1-3n) converge?

Answer 1

A. 2/3
B. -2/3
C. 0
D. Inf

Answer 2

as n --> infinity you can see that P_n becomes -2/3

at that point you can already say that the sum S_n keeps decreasing
so it won't converge.

Answer 3

I think this may be a mistake. it says 'the partial sums formula is..." and the infinite series is the limit of the partial sums. since that limit is clearly -2/3 that is what the series converges to. If the 'terms' of the series were ak = (2k+1)/(1-3k) then the sum of those terms would not converge since the limit is not zero.