Question

[Hương]

Tính tổng 

S= 1.3+3.5+5.7+......+99.101

Answer 1

[✓ ℍɠŞ_ŦƦùM $₦G ✓]

6S = 1.3(5 - 1) + 3.5(7 - 1) + 5.7(9 - 3) + ... + 99.101(103 - 97)

6S = 1.3 + 1.3.5 - 1.3.5 + 3.5.7 - 3.5.7 +..... - 97.99.101 + 99.101.103

6S = 3 + 99.101.103

6S = 3 + 1029897

6S = 1029900

S =1029900 : 6

S = 171650

Answer 2

[titanic]

Ta có S=1.(1+2)+3.(3+2)+5.(5+2)+....+99.(99+2)

=1.1+3.3+5.5+....+99.99 +1.2+3.2+5.2+...+99.2

=1²+3²+5²+...+99²+2.(1+3+5+....+99 )

=1.(2-1)+3.(4-1)+5.(6-1)+...+99.(100-1)+2.(1+3+5+...+99)

=1.2+3.4+5.6+...+99.100-1-3-5-....-99+2.(1+3+5+...+99)

=1.2+3.4+5.6+...+99.100+(1+3+5+...+99)

Xét 1.2+3.4+5.6+...+99.100 = (2-1).2+(4-1).4+(6-1).6+....+(100-1).100

=2.2+4.4+6.6+100.100-2-4-6-...-100

=2²+4²+6²+...+100²-(2+4+6+...+100)

=2².(1²+2²+3²+...+50²)-(100+2).50:2

=2².22100-2550 ( bạn tự làm thêm 1²+2²+...+100²=22100 nhé )

=85850

Do đó S= 85850-(99+1).50:2=85850-2500=83350