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 Oct6 awarded Notable Question Oct1 awarded Notable Question Sep24 awarded Autobiographer Jul2 awarded Curious Feb18 awarded Notable Question Feb10 awarded Notable Question Jan16 awarded Nice Question Dec2 awarded Popular Question Nov11 awarded Popular Question Sep27 awarded Popular Question Aug31 awarded Yearling Aug14 awarded Popular Question Feb22 accepted Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Feb22 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. Feb22 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. Feb22 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. Feb22 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. Feb22 asked Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? Jan20 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) Jan20 comment How many length n binary numbers have no consecutive zeroes ?Why we get a Fibonacci pattern? @AustinMohr I checked that.It was helpful but still doesn't clear the confusion I am facing, especially about the Fibonacci pattern.Is it OK if I let the question stay?