Question

s=1*2*3*4+2*3*4*5+....+97*98*99*100.tính s ik

Answer 1

S = 1.2.3.4 + 2.3.4.5 + 3.4.5.6+...97.98.99.100

5S = (1.2.3.4+2.3.4.5+3.4.5.6+ ... + 97.98.99.100).5

5S = 1.2.3.4.(5-0) + 2.3.4.5.(6-1)+ 3.4.5.6(7-2)+......+ 97.98.99.100.(101-96)

 5S = (1.2.3.4.5 + 2.3.4.5.6 + 3.4.5.6.7 + ....+ 97.98.99.100.101) - (0.1.2.3.4 + 1.2.3.4.5 + 2.3.4.5.6+.....+96.97.98.99.100)

 5S = 97.98.99.100.101

 S= 97.98.99.100.101/5

 S=1901009880

Answer 2

S=1*2*3*4+2*3*4*5+....+97*98*99*100

5S=1.2.3.4.5+2.3.4.5.5+...+97.98.99.100.5

5S=1.2.3.4.(5-0)+2.3.4.5.(6-1)+...+97.98.99.100.(101-96)

5S=1.2.3.4.5-0.1.2.3.4+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100

5S=(1.2.3.4.5+2.3.4.5.6+...+97.98.99.100.101)-(0.1.2.3.4+1.2.3.4.5+...+96.97.98.99.100)

5S=97.98.99.100.101

S=9505049400:5=1901009880.

Answer 3

S = 1.2.3.4 + 2.3.4.5 + 3.4.5.6+...97.98.99.100

5S = (1.2.3.4+2.3.4.5+3.4.5.6+ ... + 97.98.99.100).5

5S = 1.2.3.4.(5-0) + 2.3.4.5.(6-1)+ 3.4.5.6(7-2)+......+ 97.98.99.100.(101-96)

5S = (1.2.3.4.5 + 2.3.4.5.6 + 3.4.5.6.7 + ....+ 97.98.99.100.101) - (0.1.2.3.4 + 1.2.3.4.5 + 2.3.4.5.6+.....+96.97.98.99.100)

5S = 97.98.99.100.101

S= 97.98.99.100.101/5

S=1901009880 

Answer 4

S = 1.2.3.4 + 2.3.4.5 + 3.4.5.6+...97.98.99.100

5S = (1.2.3.4+2.3.4.5+3.4.5.6+ ... + 97.98.99.100).5

5S = 1.2.3.4.(5-0) + 2.3.4.5.(6-1)+ 3.4.5.6(7-2)+......+ 97.98.99.100.(101-96)

5S = (1.2.3.4.5 + 2.3.4.5.6 + 3.4.5.6.7 + ....+ 97.98.99.100.101) - (0.1.2.3.4 + 1.2.3.4.5 + 2.3.4.5.6+.....+96.97.98.99.100)

5S = 97.98.99.100.101

S= 97.98.99.100.101/5

S=1901009880