Explanation:- counter example: in Lan) = = (-1) :nGN sequencence of real number which is not convergent it is oscillatory. oscillate finitely be) Proofin let two sequence g so given 430 I, and I be the points of Land and [bn] respectively, J no G12 sit we have 2-₁₁ -1₁ -1, 1,-1,---- y 2-1,011 2 Nyno cans - dil 22 and | 2bn3 - 12/2€. 2 Lan) Hơn 3) kith 8 our claim 1.8. [an] tibn) cyf to i+dz ✓ N», no. we will use triangle inequality V equality. stan an-dil 올 가을 2 Bum of two 2 & ... kandbon) I LE Hence Convergent sequence is convergent. + 1 barda]