Question

1/3+1/15+1/35+1/63+1/99=？ 要用简便方法计算 告诉我过程。我记得好像要乘1

Answer 1

原式=1/2＊（1/1＊3）+1/2＊（1/3＊5）+1/2＊（1/5＊7）+1/2＊（1/7＊9）+1/2＊（1/9＊11）
=1/2＊（1/1–1/3）+1/2＊（1/3–1/5）+1/2＊（1/5–1/7）+1/2＊（1/7–1/9）+1/2＊（1/9–1/11）
=1/2＊（1/1–1/3+1/3–1/5+1/5–1/7+1/7–1/9+1/9–1/11）
=1/2＊（1–1/11）
=1/2＊10/11
=5/11

Answer 2

1/3+1/15+1/35+1/63+1/99
= 1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
= 1/2 × { 2/(1×3)+2/(3×5)+2/(5×7)+2/(7×9)+2/(9×11) }
= 1/2 × (1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
= 1/2 × (1-1/11)
= 1/2 × 10/11
= 5/11