Find (1-1 / 2 + 1 / 3-1 / 4 +...) +1/99-1/100)/{1/(1+101)+1/(2+102)+…… +1 / (50150)

Find (1-1 / 2 + 1 / 3-1 / 4 +...) +1/99-1/100)/{1/(1+101)+1/(2+102)+…… +1 / (50150)


molecule
=(1+1/2+1/3+1/4+…… +1/99+1/100)-2*(1/2+1/4+…… +1/100)
=1/51+…… +1/99+1/100
denominator
=1/2 * (1/51+…… +1/99+1/100)
primary
=1/2



1×2×3×4.99×100×101×102


That's 102!



-1+2-3+4-5+6-7+...-99+100-101=?


-1+2-3+4-5+6-7+...-99+100-101
= (-1+2)+(-3+4)+…… +(-99+100)-101
= 1×50-101
=50-101
= -51