P = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/7 + ... + 1/46 - 1/56

P = 1 - 1/56

P = 55/56 

Ta có

\(\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+...+\frac{7}{22.29}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{29}\)

\(=1-\frac{1}{29}< 1\left(dpcm\right)\)

\(\left|-30\right|-\left(2.4x\right)=-6\)

\(\Rightarrow30-8x=-6\)

\(\Rightarrow8x=30-\left(-6\right)\)

\(\Rightarrow8x=36\)

\(\Rightarrow x=\frac{9}{2}\)

Câu 1. (Sửa \(\frac{1}{2.4}\rightarrow\frac{2}{2.4}\)để có được quy luật. Còn nếu đề bài như trên thì...)

Ta có:\(\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+...+\frac{7}{22.29}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{29}\)

\(=1-\frac{1}{29}< 1\)(Vì\(\frac{1}{29}>0\))

\(\Rightarrow\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+...+\frac{7}{22.29}< 1\left(đpcm\right)\)

Vậy...

Câu 2. (Câu này làm tắt nhé)

\(\left|-30\right|-\left(2.4x\right)=-6\)

\(\Leftrightarrow30-8x=-6\)

\(\Leftrightarrow8x=36\)

\(\Leftrightarrow x=\frac{9}{2}\)

Vậy\(x=\frac{9}{2}\)

Linz

1/1.2+2/2.4+3/4.7+...+10/46/56

=1-1/2+1/2-1/4+1/4-1/7+...+1/46-1/56

=1-1/56

=55/56

1/1.2+2/2.4+3/4.7+...+10/46.56

=1-1/2+1/2-1/4+1/4-1/7+...+1/46-1/56 

=1-1/56

=55/56

fgghhh

f

D= 1/1 - 1 /2 + 1/2 - 1/4 + 1/4 - 1/7 +...+ 1/46 - 1/56

D= 1/1 - 1/56

D=  55/56

vậy D= 55/56

\(N=\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+...+\dfrac{10}{46.56}\\ N=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{46}-\dfrac{1}{56}\\ N=1-\dfrac{1}{56}\\ N=\dfrac{55}{56}\)