A= \(-\dfrac{1}{3}+\dfrac{1}{3^2}-...+\dfrac{1}{3^{100}}-\dfrac{1}{3^{101}}\)

=>3A=\(-1+\dfrac{1}{3}-...+\dfrac{1}{3^{99}}-\dfrac{1}{3^{100}}\)

=>4A=\(-1-\dfrac{1}{3^{101}}\) =>A=\(\dfrac{-1-\dfrac{1}{3^{101}}}{4}\)

Let ABC  be a triangle with othocentre H. Let M be the midpoint of BC. Let \(l\) be aline passing through A and prependicular to MH. Let A' = \(l\cap BC\). Same definations for B', C'. Prove that A'B'C' is a line prependicular to euler line of ABC