1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算
问题描述:
1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算
1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少
答
裂项法:
1/1×3+1/3×5+1/5×7+.+1/2013×2015
=1/2×(1-1/3+1/3-1/5+1/5-1/7+……+1/2013-1/2015)
=1/2×(1-1/2015)
=1/2×2014/2015
=1007/2015