Question

求解！急急急！！！要详细过程

令A=1×2+2×3+3×4+······+98×99+99×100且B=1²+2²+3²+······+98²+99²，那么A-B=？

Answer 1

A=1×(1﹢1)﹢2×(2﹢1)﹢3×(3﹢1)﹢………﹢98×(98﹢1)﹢99×(99﹢1)
=1²﹢1﹢2²﹢2﹢3²﹢3﹢……﹢98²﹢98﹢99²﹢99
A-B=1﹢2﹢3﹢…﹢98﹢99=4950

Answer 2

A-B
=1×2+2×3+3×4+······+98×99+99×100-(1²+2²+3²+······+98²+99²)
=(2-1)+2(3-2)+3(4-3)+……98（99-98）+99（100-99）
=1+2+3+……+98+99
=（1+99）×99÷2
=4950

Answer 3

A=1x2+2x3+...+99x100
=1x(1+1)+2x(2+1)+...+99x(99+1)
=1^2+1+2^2+2+...+99^2+99
=(1^2+2^2+...+99^2)+(1+2+,...+99)
故A-B=1+2+....+99=(1+99)*99/2=4950

Answer 4

解:很高兴为您解答

A-B=1*(2-1)+2*(3-2)+.........+99*(100-99)
=1+2+3+4......+99
=(1+99)*49+50
=4950
祝您学习愉快

Answer 5

A-B
= 1²+1+2²+2+3²+3+······+98²+98+99²+99 - (1²+2²+3²+······+98²+99²)
= 1+2+3+……+98+99
= 99*(1+99)/2 =4950

Answer 6

A-B=1×2-1²+2×3-2²+......+99×100-99²=1+2+3+...+99=(1+99)*99/2=4950