calculus 1 hw problem!?

y´=-3sin3x

y´´=-3^2 cos3x

y´´´= 3^3 sinx

y´´´´= 3^4 cos3x

so after four steps you return to cos 3x multiplied by 3^4

so as84 is a multiple of 4

y(84) = 3^84 cos 3x and

y(85) = -3^85sin3x

I'm going to assume that you can derive y = cos(3x) regularly.

y' = -9^1 cos(3x)

y'' = 9^2 cos(3x)

y'''= -9^3 cos(3x)

y''''= 9^4 cos(3x)

etc.

From that pattern, you can determine that

y to the nth prime = (-9)^n cos(3x)

so y to the 85th prime = (-9)^85 cos(3x)

ln(2^n) = n * ln(2), so that you've this sequence: ? a million / ln(2^n) = ? a million / (n * ln(2)) = (a million / ln(2)) * ? a million/n. because the quotient (a million / ln(2)) is only a authentic volume, your sequence converges if (and on condition that) ? a million/n does. besides the undeniable fact that it would not converge, and so neither does your sequence.