1/3+1/8+1/15+1/24+1/35+.1/9999=
问题描述:
1/3+1/8+1/15+1/24+1/35+.1/9999=
答
原式=[1/(1×3)+1/(3×5)+.+1/(98×100)]+[1/(2×4)+1/(4×6)+.+1/(99×101)]
=(1-1/3+1/3-1/5+1/5-1/7+.+1/98-1/100)+(1/2-1/4+1/4-1/6+.+1/99-1/101)
=1-1/100+1/2-1/101
=3/2-1/100-1/101