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 Nov 25 awarded Famous Question Oct 6 awarded Notable Question Oct 1 awarded Notable Question Sep 24 awarded Autobiographer Jul 2 awarded Curious Feb 18 awarded Notable Question Feb 10 awarded Notable Question Jan 16 awarded Nice Question Dec 2 awarded Popular Question Nov 11 awarded Popular Question Sep 27 awarded Popular Question Aug 31 awarded Yearling Aug 14 awarded Popular Question Feb 22 accepted Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Feb 22 comment Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Thanks for your answer Jim. Feb 22 comment Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Thanks for the answer. Feb 22 comment Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Thanks Muzzlator for your fine answer. Feb 22 comment Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? @JanDvorak Sorry for the delay in replying to you.Yes, I have got the question right.I double-check things before putting them up on this reputed maths forum. Feb 22 asked Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Jan 20 comment How many length n binary numbers have no consecutive zeroes ?Why we get a Fibonacci pattern? Thanks for answering Rob.I had given up on getting any answers for this.I have no reason to doubt your answer (Your reputation says it all)