(1-1/2²)(1+1/3²)(1-1/4²)(1+1/5²)(1-1/6²)…(1-1/2004²)(1-1/2005²).
问题描述:
(1-1/2²)(1+1/3²)(1-1/4²)(1+1/5²)(1-1/6²)…(1-1/2004²)(1-1/2005²).
答
亲,介个要用八年级上册的知识解——因式分解
原式=﹙1-1/2﹚﹙1+1/2﹚﹙1-1/3﹚﹙1+1/3﹚﹙1-1/4﹚﹙1+1/4﹚...﹙1-1/2004﹚﹙1+1/2004﹚﹙1-1/2005﹚﹙1+1/2005﹚=1/2×3/2×2/3×4/3×3/4×5/4×...×2003/2004×2005/2004×2004/2005×2006/2005
=1/2×2006/2005
=2006/4010