5. Let an be a power series with radius of convergence 2 and note that the constant term is 0. Show that there is a constant M so that for every x satisfying x ≤ 1. anx ≤ Mx|

Q: 8.) Find the interval of convergence for Š 46x-3)" n=2 n² 2^ (Hint: Use Root rest.)

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Q: · (−1)″ √2n+ 5 n³ +2n +4 n=1 t) Å sin(n) 3 n

A: Given series are: s) ∑n=1∞-1n2n+5n3+2n+4                            t)  ∑n=1∞sinnn3 To prove: Test…

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Q: Test for convergence/divergence and state the theorems used.

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Q: しx)f erentiate f メて ×ケ-X arcsin (3x -1)+ In (5x*+3) 6arctan (1-x) . メ9 fon

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Q: スnX readius of convergence. the a.) Find b.) What is intervel et convergence? (Inter the

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Q: how do we find the radius of convergence for part b)

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A: givenan=cos(3pi2 - 6n)

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A: We need to determine radius and interval of convergence.

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Q: So I worked out the question. And I got the below setup. And I got the interval of convergence as…

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A: Here we use the limit theorem.

Q: convergent (L VNRMEN

A: Given