Question

Answer 1

\(A=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(-\dfrac{3}{5}+\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)+\left(-\dfrac{7}{9}+\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)+\left(-\dfrac{11}{13}+\dfrac{11}{13}\right)+\dfrac{13}{15}\\ =0+0+0+0+0+0+\dfrac{13}{15}=\dfrac{13}{15}\)

Answer 2

\(A=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-..-\dfrac{11}{13}+\dfrac{13}{15}\) 

\(A=-\dfrac{11}{13}+\dfrac{13}{15}=\dfrac{4}{195}\)