萝莉啪啪资源网账号:多一点的脱式计算（什么都行）

解:
(2): 原式=2×{1/(3×7)+1/(7×11)+1/(11×15)+1/(15×19)+......1/(39×43)}
而1/(3×7)=1/3-2/7 1/(7×11)=2/7-3/11 1/(11×15)=3/11-4/15
1/(15×19)=4/15-5/19............1/(39×43)=10/39-11/43
∴原式=2{1/3-11/43}=20/129.
(3):
原式={1/(2＾3)}×{1/(1×2×3)+1/(2×3×4)+1/(3×4×5)+...+1/(48×49×50)}
={1/(2＾3)}×{1/(1×2)-1/(1×3)+1/(2×3)-1/(2×4)+.....+1/(48×49)-1/(48×50)}={1/(2＾3)}×{1/(1×2)+1/(2×3)+....1/(48×49)}-{1/(2＾3)}×{1/(1×3)+1/(2×4)+.....+1/(48×50)}={1/(2＾3)}×{1/1-1/2+1/2-1/3+1/4-1/5+.......1/47-1/48+1/48-1/49}-{1/(2＾3)}×{1/(1×3)+1/(2×4)+.....+1/(48×50)}={1/(2＾3)}×{1-1/49}-{1/(2＾3)}×{1/(1×3)+1/(3×5)+1/(5×7)+.......1/(47×49)+1/(2×4)+1/(4×6)+1/(6×8)+......+1/(46×48)+1/(48×50)}={1/(2＾3)}×(48/49)-{1/(2＾3)}×{1/1-2/3+2/3-3/5+3/5-4/7+....24/47-25/49+1/(2×4)+1/(4×6)+1/(6×8)+......+1/(46×48)+1/(48×50)}
=(6/49)-{1/(2＾3)}×{1-25/49})-{1/(2＾3)}×{1/(2×4)+1/(4×6)+1/(6×8)+......+1/(46×48)+1/(48×50)}=6/49-3/49-{1/(2＾5)}×{1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.....1/(24×25)}=3/49-{1/(2＾5)}×{1-1/25}
3/49-3/100=153/4900