应用公式1-1/a²=(1+1/a)(1-1/a),计算(1-1∕a²)(1-1/3²﹚﹙1-1/4²﹚…(1-1∕2003²﹚﹙1-1/2004²﹚的值
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![应用公式1-1/a²=(1+1/a)(1-1/a),计算(1-1∕a²)(1-1/3²﹚﹙1-1/4²﹚…(1-1∕2003²﹚﹙1-1/2004²﹚的值](/uploads/image/z/2106305-17-5.jpg?t=%E5%BA%94%E7%94%A8%E5%85%AC%E5%BC%8F1-1%EF%BC%8Fa%26%23178%3B%3D%EF%BC%881%2B1%EF%BC%8Fa%EF%BC%89%EF%BC%881-1%EF%BC%8Fa%EF%BC%89%2C%E8%AE%A1%E7%AE%97%EF%BC%881-1%E2%88%95a%26%23178%3B%EF%BC%89%EF%BC%881-1%EF%BC%8F3%26%23178%3B%EF%B9%9A%EF%B9%991-1%EF%BC%8F4%26%23178%3B%EF%B9%9A%E2%80%A6%281-1%E2%88%952003%26%23178%3B%EF%B9%9A%EF%B9%991-1%EF%BC%8F2004%26%23178%3B%EF%B9%9A%E7%9A%84%E5%80%BC)
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应用公式1-1/a²=(1+1/a)(1-1/a),计算(1-1∕a²)(1-1/3²﹚﹙1-1/4²﹚…(1-1∕2003²﹚﹙1-1/2004²﹚的值
应用公式1-1/a²=(1+1/a)(1-1/a),计算(1-1∕a²)(1-1/3²﹚﹙1-1/4²﹚…(1-1∕2003²﹚﹙1-1/2004²﹚的值
应用公式1-1/a²=(1+1/a)(1-1/a),计算(1-1∕a²)(1-1/3²﹚﹙1-1/4²﹚…(1-1∕2003²﹚﹙1-1/2004²﹚的值
由1-1/a²=(1+1/a)(1-1/a)可知:
1-1/3²=(1+1/3) (1-1/3)=4/3 .2/3
1-1/4²= (1+1/4 ) (1-1/4 )=5/4 .3/4
.
1-1/2004²=(1+1/2004) (1-1/2004)=2005/2004 .2003/2004
故可以知道:原式=(1-1∕a²)*2/3*4/3*3/4*5/4*4/5*...2003/2004*2005/2004
部分约掉=(1-1∕a²)*2/3*2005/2004
结果 =2005/3006(1-1∕a²)