Question

131313 / 151515 + 131313 / 454545 +131313 / 636363 + 131313 /999999

Answer 1

453583663

Answer 2

\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(=13.\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)

\(=13.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)

\(=13.\)\(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{11}\right)\)

\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{13}{2}.\frac{8}{33}\)

\(=\frac{52}{33}\)

!

Answer 3

52/33