Respuesta :
Answer:
a. False the series [tex]\sum\limits_{i=1}^\infty (-1)^n[/tex]is bounded but does not converge
b. False, xₙ = n + (-1)ⁿ⁻¹(n - 1) does not diverge to infinity but it is not bounded for n ≥ 1
c. False some bounded sequences are divergent
An example of divergent sequences, aₙ, and bₙ, such that aₙ + bₙ converges is [tex]a_n = \sum\limits_{n} \dfrac{1}{n} , \, b_n = \sum\limits_{n} \dfrac{-1}{n}[/tex]
[tex]\sum\limits_{n} \dfrac{1}{n} + \sum\limits_{n} \dfrac{-1}{n}[/tex] is convergent
Step-by-step explanation:
