Question

6/(2x4)+6/(4x6)+6/(6x8)+...+6/(98x100)

Giúp mình với!

Answer 1

\(\frac{6}{2x4}+\frac{6}{4x6}+\frac{6}{6x8}+...+\frac{6}{98x100}\)

\(=3x\left(\frac{2}{2x4}+\frac{2}{4x6}+\frac{2}{6x8}+...+\frac{2}{98x100}\right)\)

\(=3x\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=3x\left(\frac{1}{2}-\frac{1}{100}\right)=3x\left(\frac{50}{100}-\frac{1}{100}\right)=3x\frac{49}{100}\)

\(=\frac{147}{100}\)

Answer 2

6/(2×4)+6/(4×6)+6/(6×8)+...+6/(98×100)

=3× [2/(2×4)+2/(4×6)+2/(6×8)+...+

2/(98×100)

=3×(1/2 -1/4 +1/4 -1/6 +1/6 - 1/8 +...+ 1/98 - 1/100)

=3×(1/2 - 1/100)

=3×(50/100 -1/100)

=3× 49/100

=147/100

TICK CHO MÌNH NHA BẠN! KẾT VẠN VS MÌNH NHA!❣

Answer 3

\(\frac{6}{2\cdot4}+\frac{6}{4\cdot6}+\frac{6}{6\cdot8}+...+\frac{6}{98\cdot100}\)

=\(\frac{3\cdot2}{2\cdot4}+\frac{3\cdot2}{4\cdot6}+\frac{3\cdot2}{6\cdot8}+...+\frac{3\cdot2}{98\cdot100}\)

=\(\text{​​}3\cdot\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{98\cdot100}\right)\)

=\(\text{​​}3\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

=\(\text{​​}3\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)

=\(\text{​​}3\cdot\frac{49}{100}=\frac{147}{100}\)