Prove the following: 1+4+7+...+(3n – 2) n(3n-1) 2
estimate error ∞ 4n (n + 7)3n n = 1
Does sigma (3n^2-n+1)/sqrt(n^7+2n^2+5) converge or diverge using limit comparison test.
5) Test the series for convergence or divergence. n a) In 3n +1 n= b) cos(3n) 1+ (1.2)" n=1
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
3 N 5 N 7 N 3 N 3N 3 N 3 N by one or more forces as sl order of the magnitude of the pucks acceleration, from smallest to largest.
n--3n+1 (2) Explain why En=1 n1+1/n is not a p series and determine if it converges or diverges.
show that for an ideal gas 12 c(N)E 3N/2-1 VN, where c(N) is N-dependent proportionality constant. show that for an ideal gas 12 c(N)E 3N/2-1 VN, where c(N) is N-dependent proportionality constant.
Solve the recurrence relation T(n) = 2T(n / 2) + 3n where T(1) = 1 and k n = 2 for a nonnegative integer k. Your answer should be a precise function of n in closed form. An asymptotic answer is not acceptable. Justify your solution.
Solve the difference equationy(n + 2) + 4y(n + 1) +3y(n) = 3n with y(0) =0, y(1) = 1