Question

вычислите: 1/9*11+1/11*13+1/13*15+...+1/23*25

Answer 1

$frac{1}{9*11}+frac{1}{11*13}+frac{1}{13*15}+...+frac{1}{23*25}=\\frac{1}{2}*frac{11-9}{9*11}+frac{1}{2}*frac{13-11}{11*13}+frac{1}{2}*frac{15-13}{13*15}+...+frac{1}{2}*frac{25-23}{23*25}=\\frac{1}{2}*(frac{1}{9}-frac{1}{11}+frac{1}{11}-frac{1}{13}+frac{1}{13}-frac{1}{15}+...+frac{1}{23}-frac{1}{25})=\\frac{1}{2}*frac{25-9}{9*25}=frac{8}{225}$