Use the first three non-zero terms of the Maclaurin series of 1 to calculate (1-t)³ -3 3

Q: For the series The sum= 8 Ma n = 1 4n find the sum.

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Q: 1) Make a change of variable so that the following series begins with k = 5. n i=2 (−1)²+1 (i-1)²

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Q: (- 1)"9"-3 (2n + 1)! Find the sum of the series: | 0=u

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Q: Determine the sum of the following series. 113 + 69⁰ 5 3n+ 5 Σ(™)

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Q: . Evaluate the geometric series ²1 12 n=1 9.5n-1

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Q: Write the general formula for the following alternating series in the form Σ(-1)-¹an. n=1 an = 6 8 6…

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Q: Find the sum of the convent, geometric series series

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Q: (-1)"7²n Σ 32" (2n)! n=0

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Q: (b) — 2+1 Σ 32k-1 k=0

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Q: Find the sum of the first 60 terms of the series whose terms are defined by: an = 8+ (n – 1) (-3)…

A: We use concept of arithmetric progression.

Q: Find the nth term of the given infinite series for which n= 1, 2, 3, ... 1 1 +... 2x6 3x7 4x8 5x9 an…

A: Given 12×6-13×7+14×8-15×9+.....n is from 1,2,......... to infinity

Q: 6. Find the sum of the series (-1)"-1 (-1)"72n 4" (2n)! nen n=1 2 3

A: We have to find the sum of given series.

Q: (a) k=0 (-2)2k+1 3k-1

A: The given series ∑k=0∞-22k+13k-1. We have to find the sum if it is possible.

Q: Use the table of frequently used Taylor series to find the sum of the series. 2 3 4 5 X -X +X -X…

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Q: Use the geometric series power series for the following Answer Σ n=0 - r = 1 + r + r² + r³ +…

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Q: 1 Σ (k +3)(k + 4) k=1

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Q: Find the exact sum of the following series. 8∞ 1 -1 (4k-3) (4k+1)

A: A series is , a description of the operation of adding infinitely many quantities, one after the…