Question

[Vũ Hoàng Trâm Anh]

 

3	+	3	+ … +	3	=
3 . 5		5 . 7		121 . 123

Answer 1

[Đoàn Đức Hà]

\(\frac{3}{3\times5}+\frac{3}{5\times7}+...+\frac{3}{121\times123}\)

\(=\frac{3}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{121\times123}\right)\)

\(=\frac{3}{2}\times\left(\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+...+\frac{123-121}{121\times123}\right)\)

\(=\frac{3}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{121}-\frac{1}{123}\right)\)

\(=\frac{3}{2}\times\left(\frac{1}{3}-\frac{1}{123}\right)\)

\(=\frac{20}{41}\)

Answer 2

[๖ۣۜHua Phuc Vinh ✔ ( ɻɛɑm ʙáo cáo )]

\(\frac{3}{3x5}\)+ \(\frac{3}{5x7}\)+....+ \(\frac{3}{121x123}\)

(\(\frac{1}{3}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{7}\)+ ...+ \(\frac{1}{121}\)- \(\frac{1}{123}\))

=\(\frac{1}{3}\)- \(\frac{1}{123}\)

=\(\frac{40}{123}\)

Học tốt!