Question

Determine whether the sequence,y converges or diverges. If it converges, find the limit.

y=square root (n+1)

Answer 1

just give you a trick, replace some values of n to see whether it increases or decreases
if it decreases, it tends to converge
for example n =0 , --> y =1
n=1 -----> y = sqrt (2)
n=3 ---------> y = sqrt(3)
n=4 ---------> y = 2
ohohoh,,,,, it's increasing, so it diverges

Answer 2

got me?

Answer 3

thank you. I am a rookie learning limits. this topic is a bit hard for me compared to hyperbola, parabola and ellipse. Yeah I got your meaning.

Answer 4

and when you "think" it diverges, use diverge test to put it in logic and get credit

Answer 5

for your problem, I "think" it diverges, so I apply divergence test which says
If \(lim_{n\rightarrow \infty}a_n\neq0\) then \(\sum a_n\)diverges