A = 1.3 + 3.5 + 5.7 + ..+ 99.101

6A = 1.3.6 + 3.5.6 + 5.7.6 +..+ 99.101.6

6A = 1.3.(5 + 1) + 3.5.(7 - 1) +..+ 99.101.(103-97)

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

6A = 1.3 + 99.101.103

6A = 3 + 9999.103

6A = 3 + 1029897

6A = 1029900

A = 1029900 : 6

A = 171650

A = 1.3 + 3.5 + 5.7 + ..+ 99.101

6A = 1.3.6 + 3.5.6 + 5.7.6 +..+ 99.101.6

6A = 1.3.(5 + 1) + 3.5.(7 - 1) +..+ 99.101.(103-97)

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

6A = 1.3 + 99.101.103

6A = 3 + 9999.103

6A = 3 + 1029897

6A = 1029900

A = 1029900 : 6

A = 171650

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

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

A = 1×3+3×5+5×7+...+ 97×99+99×101

 6A= 1×3×6+3×5×6+5×7×6+...+97×99×6+99×101×6

6A= 1×3×(5+1)+3×5×(7-1)+5×7×(9-3)+...+97×99×(101-95)+99×101×(103-97)

6A = 1×3×5-1×3+3×5×7-1×3×5+5×7×9-3×5×7+7×9×11-5×7×9+,,,+97×99×101-95×97×99+99×101×103-97×99×101

6A= 1×3+99×101×103

6A= 1029900

A= 171650

171650

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{101}{101}-\frac{1}{101}=\frac{100}{101}\)

\(\frac{5}{1.3}+\frac{5}{3.5}+...+\frac{5}{99.101}\)

\(=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)

\(=\frac{5}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{5}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{5}{2}.\frac{100}{101}\)

\(=\frac{250}{101}\)

Đặt biểu thức là A

=> \(A=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{99}-\frac{1}{101}\right)\)

=> \(A=\frac{5}{2}\left(1-\frac{1}{101}\right)\)

=> \(A=\frac{5}{2}.\frac{100}{101}\)

=> \(A=\frac{250}{101}\)

\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\)

\(=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=\frac{5}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{5}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{5}{2}.\frac{100}{101}\)

\(=\frac{250}{101}\)

Câu 1:

A = 2.4 + 4.6 + 6.8 +...+ 98.100 + 100.102

6A = 2.4.6 + 4.6.6 +..+98.100.6 + 100.102.6

6A = 2.4.6 + 4.6.(8-2) +...+100.102.(104 - 98)

6A = 2.4.6 + 4.6.8 - 2.4.6 + ...+ 100.102.104 - 98.100.102

6A = 100.102.104

A = 100.102.104 : 6

A = 10200.104 : 6

A = 1060800 : 6

A = 176800

Câu 2:

B = 1.3 + 3.5 + 5.7 + ...+ 97.99 + 99.101

6B = 1.3.6 + 3.5.6 + ...+ 99.101.6

6B = 1.3.(5+1) . 3.5.(7-1) + ..+99.101.(103-97)

6B = 1.3.5 + 1.3.1 +3.5.7- 1.3.5 +...+99.101.103 - 97.99.101

6B = 1.3.1 + 99.101.103

6B = 3 + 9999.103

6B = 3 + 1029897

6B = 1029900

B = 1029900 : 6

B = 171650

A = 1/1.2 + 1/2.3 + 1/3.4 + .... + 1/99.100

A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.....+ 1/99- 1/100

A= 1 - 1/100

A= 99/100

AXXXXXXXXXXXXXXXXXXXXXXX

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