Recent content by drjohnsonn

Indeed. That whopper of an error was pointed out. Can't believe i did that but alas, excitement of an easy solution was blinding.

Taking the advice i was initally given - by starting with a product represation of the harmonic series has cerainly panned out better. i keptthinking "my method doesn't seem right somewhere..."

Wow that isvrry wrong indeed. Thank you

(n+1)^2 -n =n^2 +n+2 > n+1 > 2 for n≥2 and hence, adding n to the inequality yields (n+1)^2 > n+2 and it will follow That n^2>n+1

1. show that the sum of. The reciprocals of the primes is divergent. I am reposying this here under homework and deleting the inital improperly placed post 2. Theorem i use but don't prove because its assumed thw student has already lim a^1/n = 1. The gist of the approach I took is that∑1/p =...

The gist of the approach I took is that∑1/p = log(e^∑1/p) = log(∏e^1/p) and logx→ ∞ as x→∞. Proof outline: let ∑1/p = s(x). (...SO I can write this easily on tablet) and note that e^s(x) diverges since e^1/p > 1 for any p and the infinite product where every term exceeds 1 is divergent. Then...

wootwoot

Am I accurate in doing this: u = lnx dv=x^3dx du = 1/xdx v = Sx^3dx = x^4/4 and since Sudv = uv - Svdu Sx^3lnxdx = 1/4(x^4)lnx - 1/4Sx^3dx = 1/4x^4lnx - 1/16x^4 + C if i skipped something, point it out. i kind of ended up looking at the answer before i finished and hope that...

Thanks for the advice!

Thanks! I am quite a novice as of now and have not quite gotten to that point yet. I suppose I'll have to wait a bit before I finish working on this. But is the reason for having to integrate by parts that there is no general product integration rule?

Homework Statement integrating x^3lnxdxHomework Equations The Attempt at a Solution i let u = lnx du/dx = 1/x xdu = dx x=e^u substituting that, i got e^(4u)udu then i let v = 4u dv/du = 4 1/4du = dv substituting that, i got 1/4integral e^v vdv I haven't gone beyond that step yet. I was...