Question

(1 point) Determine whether the sequence (v17n + 14 - V17n} converges or diverges. If it converges, find the limit. Converges (y/n): Limit (if it exists, blank otherwise):

Answer 1

Solution :- Vian an = √17h+14 Now an Vizhtly - Janx Win +14+ Vian vitht4 +17h (VIantly) - (Vian)? Wintly tin 1] 19n+14-17n Viently tran 14 - √17ntly trian VTFn+Vizh 197 RVIAN Г 크 < Viin 7 bn= Vizn decreasing brio monto as cue can see 7 montonically lim bn = dim =0 and hoa viin kyo hence bn is convergent,

Now by using comparison test olan Ebu if bn is convergent then an is convergent ſin la convergent henee JIFn+14 an= Praved Я Convergen (r/n): Now limit, is given by 14 lim analim viantly tutin nyo neo = 14 lim nyo VIANTIGAUTIN - 14 no O home the limitin #