a)N=1.2+2.3+3.4+4.5+......+99.100
3N=1.2.3+2.3.3+3.3.4+3.4.5+......+3.99.100
3N=1.2.3+2.3.(4-1)+3.4.(5-2)+...........+99.100.(101-98)
3N=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.......+99.100.101-98.99.100
3N=99.100.101=999900
N=333300
b)P=10.11+11.12+12.13+....+29.30
3P=10.11.3+11.12.3+....+29.30.3
3P=10.11.12-9.10.11+11.12.13-10.11.12+.........+29.30.31-28.29.30
3P=29.30.31-9.10.11=25980
P=8660
R=12+22+32+....+1002
R=1.(2-1)+2.(3-1)+.........+100.(101-1)
R=1.2-1+2.3-2+3.4-3+.....+100.101-100
R=(1.2+2.3+3.4+..........+100.101)-(1+2+3+.........+99+100)
\(R=\left(N+100.101\right)-\frac{100.101}{2}\)
R=343400-5050=338350
S=100.1+2.(100-1)+3.(100-2)+......+99.(100-98)+100(100-99)
S=100.1+100.2-1.2+100.3-2.3+.......+99.100-98.99+100.100-99.100
S=100(1+2+...+100)-(1.2+2.3+....+99.100)
S=100.(100.101:2)-N
S=505000-333300=171700