Ask Experts Questions for FREE Help !
Ask
    puppylov323's Avatar
    puppylov323 Posts: 1, Reputation: 1
    New Member
     
    #1

    Apr 28, 2014, 07:08 AM
    Sequence restricted by two other sequences
    We have the following sequence a1=1 , an+1= an+ 1/an and so forth for n=1,2,…


    Show that ln n < an < n for all n>1.

    What would be the best approach for this kind of problem?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #2

    Apr 28, 2014, 07:27 AM
    The right hand side of the inequality is trivial. For the left hand side consider that the definition of ln(n) is the area under the y=1/x curve, starting at x=1 out to x=n. Compare that to an approximation of the area under y=1/x using the sum of areas of rectangles.

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Restricted Visitation [ 1 Answers ]

I am a mother of a 2 year old boy. My ex has violated the court orders by not coming to pick him up. The court told him he no longer had an extra day, now he had to settle with every other weekend. He has continuously picked up my son two hours late knowing that those were the only days that I had...

Sequences and Series Gr. 11 math- arithmetic sequence [ 4 Answers ]

The 6th term of an arithmetic sequence is x while the 11th term is y. Find the first two terms I know that it starts by x= a +5d and y= a + 10d how I don't know where to go from there. Thanks

Sequences [ 2 Answers ]

Restricted number [ 3 Answers ]

I was just wondering is there any way to obtain the number of someone who calls as 'restricted'? I keep getting these kind of calls and have no idea who they are.

Sequences [ 1 Answers ]

I need to determine a sequence or maybe a series for the depreication of a new car, it depreciates by 20% in its first year, each succeeding year it depreciates by 10%. Assume the car is still in good working condition after 10 years. If the car cost $25000, calculate the value of the car after...


View more questions Search