Ta có công thức tổng quát sau:

\(1-\frac{2}{n\left(n+1\right)}=\frac{n\left(n+1\right)-2}{n\left(n+1\right)}\)

\(=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n+2\right)\left(n-1\right)}{n\left(n+1\right)}\)

Ta có:\(\frac23\cdot\frac56\cdot\frac{9}{10}\cdot\ldots\cdot\frac{4949}{4950}\)

= \(\left(1-\frac13\right)\left(1-\frac16\right)\cdot\ldots\cdot\left(1-\frac{1}{4950}\right)\)

\(=\left(1-\frac26\right)\left(1-\frac{2}{12}\right)\cdot\ldots\cdot\left(1-\frac{2}{9900}\right)\)

\(=\left(1-\frac{2}{2\cdot3}\right)\left(1-\frac{2}{3\cdot4}\right)\cdot...\cdot\left(1-\frac{2}{99\cdot100}\right)\)

\(=\frac{\left(2+2\right)\left(2-1\right)}{2\left(2+1\right)}\cdot\frac{\left(3+2\right)\left(3-1\right)}{3\left(3+1\right)}\cdot\ldots\cdot\frac{\left(99+2\right)\left(99-1\right)}{99\left(99+1\right)}\)

\(=\frac{4\cdot1}{2\cdot3}\cdot\frac{5\cdot2}{3\cdot4}\cdot\ldots\cdot\frac{101\cdot98}{99\cdot100}\)

\(=\frac{4\cdot5\cdot\ldots\cdot101}{3\cdot4\cdot\ldots\cdot100}\cdot\frac{1\cdot2\cdot\ldots\cdot98}{2\cdot3\cdot\ldots\cdot99}=\frac{101}{3}\cdot\frac{1}{99}=\frac{101}{297}\)

Tìm x

190−(x−1)2=189

(x - 1) ² = 190 - 189

(x - 1) ² = 1

x = 1+2

x = 2

a, cái câu trả lời trước mk ghi sai

190 - (x-1)² = 189

(x - 1 ) ² = 190 - 189

(x-1)² = 1

x = 1+1

x = 2

Bài 1 :

\(S=1.3+3.5+5.7+...+99.101=3+15+35+...9999\)

Ta thấy :

\(3=2^2-1\)

\(15=4^2-1\)

\(35=6^2-1\)

.....

\(9999=100^2-1\)

\(\Rightarrow S=2^2+4^2+...+100^2-\left(1\right).\left(\left(100-2\right):2+1\right)\)

\(\Rightarrow S=\dfrac{100.\left(100+1\right)\left(2.100+1\right)}{6}-51\)

\(\Rightarrow S=\dfrac{100.101.201}{6}-51=338299\)

nhanh len nhé mik đang cần gấp ai lam trước mik tích cho

B)TK:

+)(23.36-17.36):36

=[36.(23-17)]:36

=36.6:36

=(36:36).6
=1.6
=6

b: =23-17=6

ngu dễ mà không biết làm mày là đồ con lợn

a = 4/5 nha

(3.5)^2-(16x2)^2=3^2x5^2-16^2x2^2=9x25-256x4=225-1024=-799

(39.42-37.42):42=[42.(39-37)]:42=42x2:42=1x2=2

2448:[190-(23-6)]=2448:[190-17)=2448:173=2448/173 nha Dương Ngọc Phuong Linh

\(a.3.5^2-16.2^2=3.25-16.4=75-64=11\)

\(b.\left(39.42-37.42\right):42=\left(39-37\right).42:42=2.1=2\)

\(c.2448:\left[190-\left(23-6\right)\right]=2448:\left(190-17\right)=2448:173=\frac{2448}{173}\)