My teacher assigned us the multiple choice questions from the 2003 BC Calc Ap test and there are four questions that I don't understand how to do.

10. What is the value of ∑ 2^(n+1)

?

I simplified it to ∑

When I did the sum of the geometric series from there I got 6 but the correct answer is 4.

22. What are all values of p for which the infinite series ∑

converges?

(A) p>0

(B) p>=1

(C) p>1

(D) p>=2

(E) p>2

Correct answer is E but I'm not sure where to even start on this problem.

84. A particle moves in the xy-plane so that its position at any time t is given by

and

. What is the speed of the particle when t = 3?

I figured that you needed to take the derivative of x(t) and y(t) to get dy/dx and then plug in t = 3 but apparently that isn't right. (The correct answer is 6.884)

Any help is greatly appreciated.