Give an example of a pair of series (an, bn) = and a 2 n n=1 2ºn n=1 with positive terms where lim n→∞o (2) = 0 and n=1 b diverges, but a converges. Zºn n=1
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- Proceed as in this example to rewrite the given expression using a single power series whose general term involves xk. 8 k=0 n=1 no-1- n=0 9cx^Verify that Jp+1(x) + 2J½ (x) – Jp-1(x) = 0 Tip: Compare the series of Jp+1(x) – Jp-1(x) and – 2J½(x) = 0Expand ?(x) = x2, −1 < x < 1 into an appropriate cosine orsine series
- Find two power series solutions of (x2+2)y"+5xy'-y=0 about the ordinary point x=0. Include the first three terms of each series.Consider the ODE (4 + x²)y" - 2xy' + y = 0. Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first three nonzero terms in each series.Find the sum S5 of the first 5 terms of the geometric 1 series an = 256 4 (#)' n-1 Use the formula Sn S5 = a₁(1 - p) = 1 —