Question

(1 point) Write out the first five terms of the sequence determine whether the sequence converges, n=1 and if so find its limit. (-1)+1 Enter the following information for an = (n+1)2 lim (-1)^+1 n+ (n + 1)2 (Enter DNE if limit Does Not Exist.) Does the sequence converge (Enter "yes" or "no").

Answer 1

PART(a):

The given nth term is,

(-1)"+1 an = (n + 1)'

_ z([+1) = ID I+(1-)

(-12-1 (12-911/2= q

3 (3+1)2 =

(-1) 4+1 04 = 14 + 1)2 = 25

(-1)5+1 1 05 = 15+1236

PART(b):

The given limit is,

L = lim an 22- X

(-1)+1 L = lim + (n +1)

The numerator is always +1 or -1 depending on the value of n and can be taken as constant K.

K L = lima n+ (n + 1)2

plugin the limit,

K ( +1)

L=0

PART(c):

Since the limit is finite value, the sequence converges.

The answer is yes.

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