The value of (1-sqrt{2})+(sqrt{2}-sqrt{3})+(s | vedclass

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Question

(C) The given expression is a telescoping series: $(1-\sqrt{2}) + (\sqrt{2}-\sqrt{3}) + (\sqrt{3}-\sqrt{4}) + \ldots + (\sqrt{15}-\sqrt{16})$ Observe

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

(C) The given expression is a telescoping series: $(1-\sqrt{2}) + (\sqrt{2}-\sqrt{3}) + (\sqrt{3}-\sqrt{4}) + \ldots + (\sqrt{15}-\sqrt{16})$ Observe that each term cancels out the preceding term's negative component: $= 1 - \sqrt{2} + \sqrt{2} - \sqrt{3} + \sqrt{3} - \sqrt{4} + \ldots + \sqrt{15} - \sqrt{16}$ $= 1 + (-\sqrt{2} + \sqrt{2}) + (-\sqrt{3} + \sqrt{3}) + \ldots + (-\sqrt{15} + \sqrt{15}) - \sqrt{16}$ $= 1 + 0 + 0 + \ldots + 0 - \sqrt{16}$ $= 1 - 4$ $= -3$

The value of $(1-\sqrt{2})+(\sqrt{2}-\sqrt{3})+(\sqrt{3}-\sqrt{4})+\ldots+(\sqrt{15}-\sqrt{16})$ is

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