Recent content by l888l888l888

we r not allowed to use integral tests. this is an analysis 1 class

Homework Statement prove that the series summation from n=3 to infinity of (1/(n*log(n)*(log(log(n))^p)) diverges if 0<p<=1 and converges for p>1. Homework Equations The Attempt at a Solution 2^n*a(2^n)= 1/(log(2^n)*(log(log(2^n))^p)). this is similar to the summation from n=2 to...

Homework Statement assume summation of series An converges with all An>0. Prove summation of sqrt(An)/n converges Homework Equations The Attempt at a Solution I Tried using the ratio test which says if lim as n goes to infinity of |Bn+1/Bn|<1 then summation of Bn converges. I let Bn...

that is what my classmates are saying. but i don't know exactly how to change wat i did. can you help me?

I hope so. My classmates are saying that after 30 seconds when the motor shuts off the rocket still continues upward for a while under the force of gravity (ie the rocket does not immediately return to the ground). if that is the case how would i do this problem differently?

Homework Statement A rocket is red vertically with an acceleration of 250 m/s2. After 30 seconds, the rocket's motor shuts o. Find the maximum altitude achieved by the rocket and the total time from take-o to return to the surface of the earth, assuming that the rocket's design makes...

Homework Statement let (An) be a sequence in R with |summation from n=1 to infinity(An)|< infinity. Prove lim as n goes to infinity of ((A1 +2A2+...+nAn)/n) = 0 Homework Equations The Attempt at a Solution I think |summation from n=1 to infinity(An)|< infinity means the summation...

yes. I am sorry. I made a mistake. the two solutions hsould be phi1(t) and phi2(t).

Homework Statement Show that the solution of dx/dt=f(x), x(0)=xo, f in C^1(R), is unique Homework Equations C^1(R) is the set of all functions whose first derivative is continous. F(x)=integral from xo and x (dy/f(y)) The Attempt at a Solution Assume phi1(x) and phi2(x) are both...

X2=1/4, X3=4/13, X4=13/43, X5=43/142... the sequence kinda flips up and down. it will go down, up, down,... it does not seem monotone...

Homework Statement let (Xn) be a sequence in R given by X1=1 and Xn+1=1/(3+Xn) for n>=2. prove Xn converges and find the limit. Homework Equations The Attempt at a Solution well i think using the monotone convergence theorem would help but i would have to prove that the sequence...

Great. thanks!

d(f(f(a)),f(a))<d(f(a),a). but then this contradicts the fact that d(f(a),a) is a min value?

ummmmm nothin comes to mind at this time...? if o is not the min value then d(f(a),a)>0 and we must come up with a contradiction that contradicts d(f(x),f(a))<d(x,a)?

you can infer that it attains its bounds on X. ?