Was doing my homework, came up with 5 I could not get.
I'm not too knowledgeable about the special characters you guys use to make the math problems, so I'll do my best to use normal characters.. (keep in mind that each of these problems starts with E (sum), and unless otherwise noted, it starts at n=0 and goes to infinity)
#1: (x+3)^n / (2)^n, converge or diverge, and find the sum if it converges
I was thinking of using the Geometric test, but I don't know how that works when there is an x involved (1/3 converges, but does ((1+x)/3) converge?)
#2: 1/5 + 1/8 + 1/11 + 1/14 + 1/17
I wrote up the sum (1/(5 + 3n)) where n=0, goes to infinity
I imagine then that using the p-test, it diverges? or is this not valid?
#3 asks what value of p would make the series converge?
series is (n=1, to infinity): ln(p) / n^p
I'm pretty sure you need the integral test, but how do you take the integral of ln(x)/x^p?
#4: 1+ sin(n) / 10^n
Comparison test I'm guessing? But what do you compare it to? And If you do the inequality bit (0<1+sin(n)<2), how do you determine if 2/10^n converges?
#5 (n^2 - 5n) / (n^3 + n + 1)
Can you just use L'hopital? (2n - 5) / (2n^3 +1), which becomes 2 / 6n, which diverges?
As you can tell, I am not too good with these..
I tried to make it as clear as possible, but if you're confused about the way I conveyed a question, I'll gladly try to clarify further
u = lnx
du = 1/x dx
dv = 1/(x^p)
v = (p+1)/(x^p+1)
Alright, I see what you're getting at with that one... But how do you integrate vdu?
And about that first one,
I split it up into ((x+3)/2) x ((x+3)/2))^(n-1)
I have the sum = (x+3) / (5-x), but I'm guessing that is incomplete?