11.3 Root and Ratio Test - Math 1432 Dont forget online quizzes THINK Find the number to replace the question mark 369542 is to 246359 as 172896 is to

11.3 Root and Ratio Test - Math 1432 Dont forget online...

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Math 1432 Don’t forget online quizzes. THINK: Find the number to replace the question mark. 369542 is to 246359 as 172896 is to 268179 as 417638 is to ?
Review: Geometric Series Test. The geometric series diverges if r 1 . If < r 1 , then the series converges to the sum = - 1 a S 1 r . The sum of the first n terms of a geometric series is ( 29 - = - n 1 a 1 r S 1 r . Ex. ( 29 = n n 1 3 1 2 .
Basic Divergence Test If → ∞ n n a 0 lim , then the series = n n 1 a diverges. Ex. = - + 2 2 n 1 n 1 n n
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Integral Test : If f is positive , continuous , and decreasing for x 1 and ( 29 = n a n f , then = n n 1 a and ( 29 1 x dx f either both converge or both diverge. Ex. ( 29 = n 2 1 n n ln
Basic Comparison Test: If n a 0 and n b 0 and 1) If = n n 1 b converges and n n 0 a b , then = n n 1 a converges. 2) If = n n 1 a diverges and n n 0 a b , then = n n 1 b diverges.

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