Đáp án:
Giải thích các bước giải:
Gọi tổng trên là S
S=1002−992−982−....−1=1002−(100−1)2−(100−2)2−.....−(100−99)2=1002−1002−1002−.....−1002+2.100+2.2.100+2.3.100+.....+2.99.100−12−22−32−....−992−1002+1002S=1002−992−982−....−1=1002−(100−1)2−(100−2)2−.....−(100−99)2=1002−1002−1002−.....−1002+2.100+2.2.100+2.3.100+.....+2.99.100−12−22−32−....−992−1002+1002
A=12+22+992+1002A=12+22+992+1002
=1.(2-1)+2.(3-1)+3.(4-1)+....+99.(100-1)+100.(101-1)
=1.2-1.1+2.3-1.2+3.4-1.3+...+99.100-1.99+100.101-1.100
=(1.2+2.3+3.4+...+99.100+100.101)-(1+2+3+...+100)
= [1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99) ] /3 + [(100+1).100 /2]
=[1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+100.101.102-99.10.101]/3 + 5050
=100.101.102/3 + 5050
=348450
⇒S=−99.1002+2.100.99.100−A=641550
