20. (a) Suppose that (u2n) and (u2n+1) converge to the same limit l. Prove that (un)converges to l.(b) Find a sequence (un) such that (un) and (un+1) are convergent, but (Un) isdivergent.(c) Suppose that (u2n), (U2n+1) and (u3n) are convergent. Show that (un) is alsoconvergent.

Name: 20. (a) Suppose that (u2n) and (u2n+1) converge to the same limit l.
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Description: 20. (a) Suppose that (u2n) and (u2n+1) converge to the same limit l. Prove that (un)converges to l.(b) Find a sequence (un) such that (un) and (un+1) are convergent, but (Un) isdivergent.(c) Suppose that (u2n), (U2n+1) and (u3n) are convergent. Show

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20. (a) Suppose that (u2n) and (u2n+1) converge to the same limit e. Prove that (un) converges to l.

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Chapter2: Second-order Linear Odes

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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.

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20. (a) Suppose that (u2n) and (u2n+1) converge to the same limit l. Prove that (un)
converges to l.
(b) Find a sequence (un) such that (un) and (un+1) are convergent, but (Un) is
divergent.
(c) Suppose that (u2n), (U2n+1) and (u3n) are convergent. Show that (un) is also
convergent.

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