\(\frac{1.1}{1.2}.\frac{2.2}{2.3}\frac{3.3}{3.4}...\frac{100.100}{100.101}\)

\(=\frac{\left(1.2.3...100\right).\left(1.2.3...100\right)}{\left(1.2.3...100\right).\left(2.3...101\right)}\)

\(=\frac{1}{1.101}\)

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

k cho mk nha

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.......\frac{99^2}{99.100}.\frac{100^2}{100.101}\)

\(=\frac{1.2.3.....100}{1.2.3....100}.\frac{1.2.3....100}{2.3.4...101}\)

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

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{99^2}{99.100}.\frac{100^2}{100.101}\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{99}{100}.\frac{100}{101}\)

\(=\frac{1.2.3...99.100}{2.3.4...100.101}\)

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

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.............\frac{100^2}{100.101}\)

\(=\frac{1.1}{1.2}.\frac{2.2}{2.3}.\frac{3.3}{3.4}..........\frac{100.100}{100.101}\)

\(=\frac{\left(1.2.3............100\right).\left(1.2.3..........100\right)}{\left(1.2.3..........100\right)\left(2.3.4...........101\right)}\)

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

tao dóe biet

a,1^2/1.2 . 2^2/2.3 . 3^2/3.4 ... 99^2/99.100 . 100^2/100.101

= 1/2 . 2/3 . 3/4 ... 99/100 . 100/101

=( 2.3.4....100/2.3.4...100) . 1/101

= 1 . 1/101

=1/101

ý b tương tự nhé !

Bạn kia đéo biết thì thôi xen vào làm gì?

\(A=\frac{1^2}{1.2}.\frac{2^2}{2.3}.....\frac{100^2}{100.101}=\frac{\left(1.2.....100\right).\left(1.2.....100\right)}{\left(1.2.....100\right).\left(2.....101\right)}=\frac{1}{101}\)

=2(1/1.2+1/2.3+...+1/100.101)

=2(1/1-1/2+1/2-...+1/100-1/101)

=2(1-1/101)

=2.100/101

=200/101

2/1.2+2/2.3+2/3.4+...+2/100.101

= 2(2/1.2+2/2.3+2/3.4+...+2/100.101)

= 2(1/1.2+1/2.3+1/3.4+...+1/100.101)

= 2(1/1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101)

= 2.(1/1-1/101)

= 2.100/101

= 200/101

Cho mình 1 đ-ú-n-g nha bạn

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{100^2}{100.101}\)

\(=\frac{1.1.2.2.3.3...100.100}{1.2.2.3.3.4.4...100.101}\)

\(=\frac{\left(1.2.3...100\right)\left(1.2.3...100\right)}{\left(1.2.3..100\right)\left(2.3.4...101\right)}=\frac{1}{101}\)