Question

Tính nhanh

S=1/2.3+1/3.4+1/4.5+....+1/49.50

 

Answer 1

\(S=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+.......+\frac{1}{49\cdot50}\)

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.......+\frac{1}{49}+\frac{1}{50}\)

\(S=\frac{1}{2}-\frac{1}{50}\)

\(S=\frac{25}{50}-\frac{1}{50}\)

\(S=\frac{24}{50}=\frac{12}{25}\)

ai k mh mh k lại

k cho mh nha

Answer 2

S=1/2.3+1/3.4+1/4.5+....+1/49.50

=\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...........+\frac{1}{49x50}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..........+\frac{1}{49}-\frac{1}{50}\)

=\(\frac{1}{2}-\frac{1}{50}\)

=\(\frac{24}{50}\) mình cũng ko chắc đúng nhưng đây là cách giải của mình

Answer 3

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{12}{25}\)

Answer 4

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(S=1-\frac{1}{50}\)

\(S=\frac{49}{50}\)

Answer 5

t lại đi mina

Answer 6

S=1/2-1/3+1/3-1/4+1/4+...+1/49-1/50

S=1/2-1/50

S=12/25

Answer 7

\(S=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{49\cdot50}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(s=\left(\frac{1}{2}-\frac{1}{50}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+...+\left(\frac{1}{49}-\frac{1}{49}\right)=\left(\frac{25}{50}-\frac{1}{50}\right)+0+...+0=\frac{24}{50}=\frac{12}{25}\)Vậy S=12/25

Answer 8

\(S=\frac{1}{2.3}+\frac{1}{3.4}+.................+\frac{1}{49.50}\) 

=> \(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{49}-\frac{1}{50}\) 
=> \(S=\frac{1}{2}+\left(\frac{-1}{3}+\frac{1}{3}\right)+.........+\left(\frac{-1}{49}+\frac{1}{49}\right)-\frac{1}{50}\)  
=> \(S=\frac{1}{2}-\frac{1}{50}\) 

=> \(S=\frac{24}{50}\)