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...

Homework Statement An architect who is building a skyscraper comes to see you. The architect wishes to place a safety net on the skyscraper, to prevent damage or injury should any of the building's decorative features be dislodged by wind or other forces. What advice can you give her on...

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)?