For a, look at the . What happens when n goes to infinity there?
For b, concentrate on the sin portion.
For c, set equal to y and natural log.
For d, I think this should work
Which ones are convergent and which are divergent and what are the limits of the convergent ones?
a) lim (as n goes to infinity) of (-1)^n sin(n)/n
b) lim (as n goes to infinity) of (-1)^n sin(1/n)
c) lim (as n goes to infinity) of n^(1/n) (L'Hospital's Rule)
d) lim (as n goes to infinity) a(sub)n where a1 = sqrt(2) , a2 = sqrt(2sqrt(2)), a3 = sqrt(2sqrt(2sqrt2))) , an+1 = sqrt(2an)
i think a is divergent becaue of the alternator and b converges to 0 because of squeeze theorem. Is this right? And how do i find the other two?
The function is represented here...
There is only one 'attractive fixed point' in and because is [see 'red line'...] any will generated a sequence monotonically convergent at ...