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If Σuk and Σvk are convergent series, then Σ(u + Uk) and Σ(uk - vk) are convergent series and the sums of these series are related by (uk + Uk) = Σuk + Συκ k=1 k=1 ∞ ∞ Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary- k=1 ∞ Σ(uk - Uk) = Συκ-Συκ k=1 k=1 k=1 1 1 (a) · ( 1² + ² ) + ( + + + ²) + + (1) 92 1 10k 1 ka) - k(k + 1), = +.

If Σuk and Σvk are convergent series, then Σ(u + Uk) and Σ(uk - vk) are convergent series and the sums of these series are related by (uk + Uk) = Σuk + Συκ k=1 k=1 ∞ ∞ Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary- k=1 ∞ Σ(uk - Uk) = Συκ-Συκ k=1 k=1 k=1 1 1 (a) · ( 1² + ² ) + ( + + + ²) + + (1) 92 1 10k 1 ka) - k(k + 1), = +.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If Σu and Συκ are convergent series, then Σ(uk + vk) and Σ(uk - vk) are convergent series and the sums of these series are related by Σ(uk + Uk) = Συκ + Συκ k=1 k=1 00 Σ(uk - *k) = Συκ k=1 k=1 Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary. (~) ( + ) + ( ₁ + ²) + + (₁ - }). 1 2 ... + + 9 92 2k bk (b) Σ(141) - = 10k k(k + 1) Συκ k=1 k=1 ... –
Transcribed Image Text:If Σu and Συκ are convergent series, then Σ(uk + vk) and Σ(uk - vk) are convergent series and the sums of these series are related by Σ(uk + Uk) = Συκ + Συκ k=1 k=1 00 Σ(uk - *k) = Συκ k=1 k=1 Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary. (~) ( + ) + ( ₁ + ²) + + (₁ - }). 1 2 ... + + 9 92 2k bk (b) Σ(141) - = 10k k(k + 1) Συκ k=1 k=1 ... –
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