Question

4/(3*7) + 4/ (7*11) +...+ 4/ [ ( 3x - 1) ( 3x + 3 ) ] = 3/10

Giúp mình với! Có lời giải nghen, hay thì mình tick!

Answer 1

\(\frac{4}{3x7}\)+\(\frac{4}{7x11}\)+....+\(\frac{4}{\left(3x-1\right)\left(3x+3\right)}\)= \(\frac{3}{10}\)

=\(\frac{1}{3}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{11}\)+...+\(\frac{1}{3x-1}\)- \(\frac{1}{3x+3}\)= \(\frac{3}{10}\)

=> \(\frac{1}{3}\)- \(\frac{1}{3x+3}\)=\(\frac{3}{10}\)

=> \(\frac{1}{3}\)-\(\frac{3}{10}\)=\(\frac{1}{3x+3}\)

=> \(\frac{1}{30}\)=\(\frac{1}{3x+3}\)

nhân chéo ta có: 3x+3=30

=> 3x=30-3=27

=> x= 27:3

=>x=9

nhé ^_^ mơn nhiều