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cakesmckakes
Lv 4
cakesmckakes asked in Science & MathematicsMathematics · 9 years ago

Does the sequence converge? Is it also Cauchy?

Let a_1=1 and let a_(k+1)=1/(a_k)

Determine whether a_k converges or diverges. Also, if it converges, is it Cauchy?

Note: "a_k" means "a subscript k"

1 Answer

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  • No Mythology
    Lv 7
    9 years ago
    Favorite Answer

    Your sequence is just {1, 1, 1, 1, ....}. Yeah it converges, and it is Cauchy.

    FYI: Convergent sequences are always Cauchy. The converse holds for sequences in a complete space.

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