Time remaining:
perfect answer only

label Mathematics
account_circle Unassigned
schedule 0 Hours
account_balance_wallet $5

Oct 19th, 2017

As n increases...

If we look on the top line of the fraction,

n is slowly increasing

in will therefore also be slowly increasing in magnitude

and n to the i th power with also be increasing in magnitude

This is happening at a fairly constant rate, since if we factorise out n in the top bracket we get:

n( 1 + i + n^(i - 1) )

The interesting part of the sequence is the denominator.

i to the n means the square root of -1 to the nth power

If we have i squared then that is -1

But i to the power of 4 is 1

This idea repeats: i^6 is -1, but i^8 is 1

i.e. if n is a multiple of 4 then the end result is positive and therefore the result in the sequence is positive.

But if the power- if n- is a multiple of 2 but not of four then the result will be negative

Therefore the sequence will fluctuate up and down increasing in magnitude as the sequence continues- as the numerator is larger and larger and the constant flipping of the bottom turns it from positive to negative and back again.

The sequence is divergent.

Jan 10th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
Oct 19th, 2017
Oct 19th, 2017
Oct 20th, 2017
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer