Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

(1+2(1+3(1+4(....)^0.5)^0.5)^0.5)^0.5

MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
sqrt(1+3sqrt(1+3sqrt(1+(...)))) > y > sqrt(1+2sqrt(1+2sqrt(...))) Which means LHS is solution of y^2-3y-1 and RHS is solution of y^2-2y-1 => (3+sqrt(13))/2 > y > 1+sqrt(2) => 3.3 > y > 2.414 Siddhi, I think the left hand side of your inequality is incorrect -- the factor is usually larger than 3. I don't know the answer to this question, but my guess is that the value is infinite. The square root of a very large number is still fairly large, and if you multiply that by anothr large number and take the square root you'll get an even larger number than the first square root. Perhaps you can program a computer to try this for some large, finite sequence. Hburgiel, No its a finite number, The factors become more and more insignificant as the proceed INTO the roots, So in reality the number is converging to a finite number. PS: I tried on google with increasing finite number and the number increases but with a decreasing slope, decreasing rate. (I felt it to be converging to the finite number 3) amogh, though the number increases but with decreasing slope, decreasing rate, it doesn't mean that the number is not infite --- consider the harmony series \sum{\frac{1}{n}} Yes you are right luckyted, My explanation was not right but it is converging, Sorry I can't prove it but that's what I noticed! yes amogh,u r write...its a finite number n its 3 but how do u solve it or guess? I'm thinking on it, I'll post it here if I come up to anything good! Based on Siddhi's work, it follows that, there exists one x such that, and 2 sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+........)))) (y^2-1)/2 > y y^2-2y-1>0 and we have y>0 these two simultaneous conditions leads us to a solution that y>2.414. See first of all, its obvious why y> sqrt(1+2 sqrt(1+ 2 sqrt(...))), isn't it? OK, I'm back from work. sqrt{3} > sqrt{sqrt{4}} > sqrt{sqrt{sqrt{5}}} ..... So what I'm trying to say is that the significance of the numbers goes on decreasing from left to right, ie. into the roots. sqrt{n}>sqrt{sqrt{n+1}} only when n is finite no, in case of any infinite no how can you say this!!!! the given series has no termination.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question