已知：|x|=4,|y|=3,且x,y同号,求1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)已知：|x|=4,|y|=3,且x,y同号,求1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)

Question

已知：|x|=4,|y|=3,且x,y同号,求 1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)
已知：|x|=4,|y|=3,且x,y同号,求
1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)

Answer 1

当x=4时,y=3,
1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)
=1/9*8+1/10*9+…+1/224*223
=1/8-1/9+1/9-1/10+…+1/223-1/224
=1/8-1/224
=27/224
当x=-4时,y=-3
1/(x+5)(y+5)+1/(x+6)(y+6)+…+1/(x+220)(y+220)
=1/1*2+1/2*3+…+1/216*217
=1-1/2+1/2-1/3+…+1/216-1/217
=1-1/217
=216/217