A=1.2+2.3+...+49.50

3A=1.2.3+2.3.3+...+49.50.3

3A=1.2.(4-1)+2.3.(5-2)+....+49.50.(51-48)

3A=1.2.4-1.2.1+2.3.5-2.3.2+...+49.50.51-49.50.48

3A=49.50.51

=>A=49.25.51

=>A=62475

A=1.2+2.3+...+49.50

3A=1.2.3+2.3.3+...+49.50.3

3A=1.2.(4-1)+2.3.(5-2)+....+49.50.(51-48)

3A=1.2.4-1.2.1+2.3.5-2.3.2+...+49.50.51-49.50.48

3A=49.50.51

=>A=49.25.51

=>A=62475

3S=(1.2+2.3+3.4+...+49.50).3

3S=1.2.3+2.3.3+3.4.3+...+49.50.3

3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+49.50.(51-48)

3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50

3S=49.50.51

S=17.49.50

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

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

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

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

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

ai k mh mh k lại

k cho mh nha

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

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

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

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

A=2(1-3)+4(5-3)+ 6(5-7)+...+50(49-57)

A=-4-8-12-...-100 = -(4+8+12+...+100) (tính tổng cấp số cộng)

1/2 + 1/2 x 3 + 1/3 x 4 + ........+ 1/49 x 50

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

= 1/2 - 1/50

= 12/25

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

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

Vậy A=49/50

Công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

3.s =1.2.3+2.3.3 +3.4.3+........+49.50

3s= 1.2 .3+ 2.3.(4-1) +.....+ 49.50( 51-48)

3s=49.50.51

3s=124950

s= 124950chia 3

s= 41650

chia=/ or chia= :

\(Dear,Ph\text{ạm}Nguy\text{ễn}H\text{à}Vi \)z=312579 21yiauy9-6 m4n 8bv38 vfffffffffffffffffduvfeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeesjk8bxhcngtrfhftoxd9 rn r r r r r xcvnoiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiim89;pllllhj54rtxc rdt76nb5cvrt88888f9 r5fc7y p88;g bạn giỏi quá

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

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

\(=1-\frac{1}{50}< 1\) (đpcm)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\)

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

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

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

\(\Rightarrow\) Quy đồng phân số và 1 là : \(\frac{49}{50}\) và \(1\)

Giữ nguyên phân số \(\frac{49}{50}\)

Ta có : \(\frac{1}{1}=\frac{1.50}{1.50}=\frac{50}{50}\)

\(\Rightarrow\frac{49}{50}< \frac{50}{50}\left(đpcm\right)\)

đặt A = 1.2. + 2.3 + 3.4 + ... + 49.50

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 49.50.3

3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 49.50.(51 - 48)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 49.50.51 - 48.49.50

3A = 49.50.51

A = 41650

Thay vào ta được

41650 + 1/2x = 40642

=> 1/2x = 1008

=> x = 2016