Question

[Duong Tien Phong]

 

4	+	4	+ … +	4	=
9 x 10	10 x 11	108 x 109

Answer 1

[Nguyễn Việt Hoàng]

\(\dfrac{4}{9\times10}+\dfrac{4}{10\times11}+...+\dfrac{4}{108\times109}\)

\(=4\left(\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+....+\dfrac{1}{108}-\dfrac{1}{109}\right)\)

\(=4\times\left(\dfrac{1}{9}-\dfrac{1}{109}\right)\)

\(=\dfrac{400}{981}\)

Answer 2

[Mai Hoàn]

9×104​+10×114​+...+108×1094​

=4\left(\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+....+\dfrac{1}{108}-\dfrac{1}{109}\right)

=4\times\left(\dfrac{1}{9}-\dfrac{1}{109}\right)

=\dfrac{400}{981}