裂项求和法1/3+1/15+1/35+1/63+1/99=?
问题描述:
裂项求和法
1/3+1/15+1/35+1/63+1/99=?
答
=1/(1*3)+1/(3*5)+....1/(9*11)
=1/2*[1/1-1/3+1/3-1/5+....+1/9-1/11]
=1/2*(1-1/11)
=5/11
答
1/3+1/15+1/35+1/63+1/99 =[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]÷(3-1) =[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]÷2 =(1-1/11)÷2 =5/11 裂项分拆:1/(a×b)=(1/a-1/b)÷(b-a)...