MAT1505-03/04 15F Quiz 9 Print Name (Last, First) __________________ , _______________|____Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC).1. Use the geometric series algebra manipulation trick to find a power series for 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. What is its radius of convergence?2. Find the radius of convergence and the interval of convergence (use interval notation) for the power series LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkrbXVuZGVyb3ZlckdGJDYnLUkjbW9HRiQ2LVEmJlN1bTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictRiM2Ji1JI21pR0YkNiVRIm5GJy8lJ2l0YWxpY0dGPC9GM1EnaXRhbGljRictRi82LVEiPUYnRjIvRjZRJmZhbHNlRicvRjlGWS9GO0ZZL0Y+RlkvRkBGWS9GQkZZL0ZERlkvRkZRLDAuMjc3Nzc3OGVtRicvRklGW28tSSNtbkdGJDYkUSIwRidGMkYyLUYjNictRi82LVEoJmluZmluO0YnRjJGWEZaRmVuRmZuRmduRmhuRmluRkUvRklGR0ZRLyUrZm9yZWdyb3VuZEdRLFsyMDAsMCwyMDBdRicvJSxwbGFjZWhvbGRlckdGPEZTRmluLyUsYWNjZW50dW5kZXJHRlktSSZtZnJhY0dGJDYoLUklbXN1cEdGJDYlLUZONiVRInhGJ0ZRRlMtRiM2JUZNRlFGUy8lMXN1cGVyc2NyaXB0c2hpZnRHRmBvLUYjNictRl5vNiRRIjNGJ0YyLUkobWZlbmNlZEdGJDYkLUYjNidGTS1GLzYtUSIrRidGMkZYRlpGZW5GZm5GZ25GaG5GaW4vRkZRLDAuMjIyMjIyMmVtRicvRklGaXEtRl5vNiRRIjJGJ0YyRlFGU0YyLUZicDYlRltyRmdwRmlwRlFGUy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXIvJSliZXZlbGxlZEdGWUYy. Justify your claims.
solution1. 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. 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When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSUmcG07RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlMtSSNtbkdGJDYkUSIyRidGOUY5: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For large LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= this looks like a multiple of a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= = 1series (harmonic series) which diverges because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is not greater than 1.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 is an alternating series whose nth term in absolute value is decreasing and goes to zero, so it converges.The interval of convergence is therefore 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