I need help in solving an initial-value problem and a few series problems (Especially on #45 & #46). I don't really understand how to do the series problems...majority of the time. An explanation would be great as well. Thank you for your time.
#20) Solve the initial-value problem.
(9 + e^x)dy/dx + e^xy = sin x, y(0) = 1/10
#45) Determine whether the given series converges or diverges.
(∞ on top of summation symbol) (n = 1 under the summation symbol) ∑ [cos(4/n) - cos(4/(n+1)]
If it converges, find its sum.
#39) Consider the following series.
(∞ on top of summation symbol) (n = 1 under the summation symbol) ∑ (1+9^n)/8^n
(a) Determine whether the series is convergent or divergent.
(b) If it is convergent, find its sum.
#46) Determine whether the given series converges or diverges.
(∞ on top of summation symbol) (n = 1 under the summation symbol) ∑ ln(n/n+1)
If it converges, find its sum.
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