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Category: Geometry

In-a-equilateral-triangle-ABC-whose-side-is-a-the-points-M-and-N-are-taken-on-the-side-BC-such-that-the-triangles-ABM-AMN-and-ANC-have-the-same-perimeter-Calculate-the-distances-from-vertex-A-to-

Question Number 68664 by Maclaurin Stickker last updated on 14/Sep/19 InaequilateraltriangleABCwhosesideisa,thepointsMandNaretakenonthesideBC,suchthatthetrianglesABM,AMNandANChavethesameperimeter.CalculatethedistancesfromvertexAtopointsMandN.(solveindetail.)

Question-68611

Question Number 68611 by TawaTawa last updated on 14/Sep/19 Answered by mind is power last updated on 15/Sep/19 1r24=14(r2)14(r+2)$$\Rightarrow\sum_{{r}=\mathrm{3}} ^{\mathrm{100}} \frac{\mathrm{1}}{{r}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}}\Sigma\left(\frac{\mathrm{1}}{{r}−\mathrm{2}}−\frac{\mathrm{1}}{{r}+\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{99}}−\frac{\mathrm{1}}{\mathrm{100}}−\frac{\mathrm{1}}{\mathrm{101}}−\frac{\mathrm{1}}{\mathrm{102}}\right)…