Question

1/ 3x9 + 1/ 9x15 + 1/ 15x21 + 1/ 21x27 + ... + 1/39 x 45
Ai làm nhanh giúp mk vs mk đang gấp lắm

Answer 1

\(\dfrac{1}{3\times9}+\dfrac{1}{9\times15}+\dfrac{1}{15\times21}+\dfrac{1}{21\times27}+...+\dfrac{1}{39\times45}\)
\(=\dfrac{1}{6}\times\left(\dfrac{6}{3\times9}+\dfrac{6}{9\times15}+\dfrac{6}{15\times21}+\dfrac{6}{21\times27}+...+\dfrac{6}{39\times45}\right)\)
\(=\dfrac{1}{6}\times\left(\dfrac{1}{3}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{27}+...+\dfrac{1}{39}-\dfrac{1}{45}\right)\)
\(=\dfrac{1}{6}\times\left(\dfrac{1}{3}-\dfrac{1}{45}\right)\)
\(=\dfrac{1}{6}\times\dfrac{14}{45}\)
\(=\dfrac{7}{135}\)
#AvoidMe

Answer 2

=1/6(6/3*9+6/9*15+...+6/39*45)

=1/6(1/3-1/9+1/9-1/15+...+1/39-1/45)

=1/6*14/45

=14/270=7/135