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    Infinite Series : Convergence and Divergence (8 Problems)

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    1)
    a) Prove that

    N
    ∑ 1/n(n+1) = 1- (1/N+1)
    n=1

    Hence, or otherwise, determine whether the following infinite series is convergent or divergent:

    b) Determine whether each of these infinite series are convergent or divergent. Justify your answer
    ∞
    i) ∑ n²/n³ +10³
    n=1

    ∞
    ii) ∑ 1/tan‾ ¹(n)
    n=1

    ∞
    iii) ∑ (-1)ⁿ/In(n)
    n=2

    2)
    a) Express (1/n+1) - (1/n+3) as a single fraction

    using this result, or otherwise, prove that

    ∞
    ∑ 1/(n² +4n+3) = ½{(3/2)-(1/n+2)-(1/n+3)}
    n=0

    Hence determine whether the infinite series

    ∞
    ∑ 1/(n² +4n+3)
    n=0
    is convergent or divergent, justify your determination

    b) The series
    ∞
    ∑ ( n+7)/(4n-1)
    n=1
    is divergent. Explain in detail why this is the case

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    https://brainmass.com/math/real-analysis/infinite-series-convergence-and-divergence-8-problems-42068

    Solution Summary

    The convergence or divergence of series is investigated. The solution is detailed and well presented.

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