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(1) State the Bolzano–Weierstraß theorem. Prove that the following sequences have convergent subsequences: (a) {sin(n)} (b)...

(1) State the Bolzano–Weierstraß theorem. Prove that the following sequences have convergent subsequences: (a) {sin(n)} (b) 2n 2+5n+6 n2+12n+20 cos(n 2 )

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