bạn rảnh quá nhỉ

khoảng cách là :  2-1 =1

Số số hạng : ( 15-1) chia 1 +1=15

tổng dãy : ( 15 +1 )nhân 15 chia 2 =120

đáp số : 120

vẽ đường phụ ik!

lp1 chưa có đạng này

\(\dfrac{6}{1\cdot3}+\dfrac{6}{3\cdot5}+...+\dfrac{6}{\left(n-2\right)n}\\ =3\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{\left(n-2\right)n}\right)\\ =3\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{n-2}-\dfrac{1}{n}\right)\\ =3\left(1-\dfrac{1}{n}\right)\\ =3\cdot\dfrac{n-1}{n}\)

\(\overline{X}=\dfrac{7\cdot3+8\cdot?+9\cdot6+10\cdot3}{3+?+6+3}=\dfrac{105+8?}{12+?}=8,45\\ \Rightarrow8,45\left(12+?\right)=105+8?\\ 101,4+8,45?=105+8?\\ 0,45?=3,6\\ ?=8\)

\(M=\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+...+\dfrac{1}{1+2+3+...+59}\\ =\dfrac{1}{\dfrac{3\cdot4}{2}}+\dfrac{1}{\dfrac{4\cdot5}{2}}+...+\dfrac{1}{\dfrac{59\cdot60}{2}}\\ =\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{59\cdot60}\\ =2\left(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{59\cdot60}\right)\\ =2\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{59}-\dfrac{1}{60}\right)\\ =2\cdot\dfrac{19}{60}\\ =\dfrac{38}{60}< \dfrac{40}{60}=\dfrac{2}{3}\)

\(\left|x\right|+x=0\\ x\ge0\Rightarrow\left|x\right|=x\\ \left|x\right|+x=0\\ x+x=0\\ 2x=0\\ x=0\\ x< 0\Rightarrow\left|x\right|=-x\\ \left|x\right|+x=0\\ -x+x=0\\ 0=0\text{(luôn đúng)}\)

Vậy \(x\le0\)

\(x+\left|x\right|=2x\\ x\ge0\Rightarrow\left|x\right|=x\\ x+\left|x\right|=2x\\ x+x=2x\\ 2x=2x\text{(luôn đúng)}\\ x< 0\Rightarrow\left|x\right|=-x\\ x+\left|x\right|=2x\\ x+\left(-x\right)=2x\\ 0=2x\\ x=0\)

Vậy \(x\ge0\)

\(B=\dfrac{5^2}{2\cdot3\cdot4}+\dfrac{5^2}{3\cdot4\cdot5}+\dfrac{5^2}{4\cdot5\cdot6}+...+\dfrac{5^2}{48\cdot49\cdot50}\\ =\dfrac{5^2}{2}\cdot\left(\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+\dfrac{2}{4\cdot5\cdot6}+...+\dfrac{2}{48\cdot49\cdot50}\right)\\ =\dfrac{25}{4}\cdot\left(\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+...+\dfrac{1}{48\cdot49}-\dfrac{1}{49\cdot50}\right)\\ =\dfrac{25}{4}\cdot\left(\dfrac{1}{6}-\dfrac{1}{2450}\right)\\ =\dfrac{25}{4}\cdot\dfrac{611}{3675}\\ =\dfrac{611}{588}\)

0(vì số thứ nhất = số thứ hai )