Question

1. For each of the following sequences, determine whether it converges. If so, find the limit. 2n+1 5n-2 a. b. 4. =(-1)"." 2n 2"-1 c. n

Answer 1

is encists and If lim an we say n00 finite else it diverges the sequence converges an Intl 50-2 lim an lim 2nt) 50-2 n> no Dividing both numerator and ner denominator by n 2 lim no 5 nis Applying limit, lim an E . Constant Grin -> no Answer: Converges Ö 2 5 (6 lim an = n7 nyo At an= (-1)? 0-1 20. lim 1-1)" (n-1) 2n Due to to +)" the sequence a single value no exist and we can say Answers Diverges as اور ان پر does not approach lim an does not that sequence an diverges no

с An-22_) Applying limit we get we get to form lim an lim 12" n-> n-700 n Rule Ľ Hospital .. Applying on d =lim -1) an n 700 (n) an =lim 2 ln (2) -0 nyoo نم =lim na 2” ( n 2) On applying limit, 20 : lim an and Sequence :: en diverges n 100 Answer: Diverges