Comparing sequences with a parameter For what values of adoes the sequence {n!} grow faster than the sequence {nan}?(Hint: Stirling’s formula is useful: n! ≈ √(2πn) nne-n, for large values of n.)

Q: (-1)³ 3j² + 5j

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A: given  ∑1∞ (x-3)nn

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Q: 4n2-11 Q2. Determine if the sequence converges, and if so find its limi 12n2+4n-8.

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Q: 2. (x+ 2)? E nan(x + 2)"-4 – E nan(x + 2)" n=3 n=1

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Q: 7. The series A. E converges when 2n A.r>1 B.r<1 C.r=1 D.r=0

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A: Solution:

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A: The difference between formulas of order of convergence O(hk) and o(hk) is discussed below.

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Q: =1 2n + 5

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Q: 6. 3n2 + 2 n=1

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Q: НOMEWORK Determine the series converges or diverges, and if it converges find the sum k! (2k)! k=0

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Q: j=1 (−1)ª 3j² + 5j

A: Given series is ∑j=1∞−1j3j2+5j. Alternate series test:- Let an be a sequence of positive real number…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.