Question

一道初中数学题很急 谢谢

3/2*2+3/2*2*3+3/2*3*4+...+3/2*2004*2005

Answer 1

3/2×2+3/2×2×3+3/2×3×4+...+3/2×2004×2005
=(3/2)(1/1×2+1/2×3+1/3×4+...+1/2004×2005)
=(3/2)(1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004+1/2004-1/2005)
=(3/2)(1-1/2005)
=(3/2)(2004/2005)
=3006/2005

Answer 2

3/2*2+3/2*2*3+3/2*3*4+...+3/2*2004*2005
=3/2*(1/2+1/2*3+1/3*4+...+1/2004*2005)
=3/2*(1/2+1/2-1/3+1/31/4+1/4-1/5+...+1/2004-1/2005)
=3/2*2004/2005=3006/2005

Answer 3

3/2[1+1/2*3+1/3*4+...+1/2004*2005]
=3/2[1+1/2-1/3+1/3-1/4+....+1/2003-1/2004+1/2004-1/2005]
=3/2[1+1/2-1/2005]

Answer 4

原式=1.5*(1/1*2+1/2*3+.......+1/2004*2005)=1.5*(1-1/2+1/2-1/3+..........+1/2004-1/2005)=1.5*2004/2005=3006/2005,