\(B=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{50}\cdot\dfrac{50\cdot51}{2}\)

\(=1+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{51}{2}\)

\(=\dfrac{50\cdot\dfrac{\left(51+2\right)}{2}}{2}=50\cdot\dfrac{53}{4}=662.5\)

\(E=-\dfrac{1}{3}\cdot\left(1+2+3\right)-\dfrac{1}{4}\left(1+2+3+4\right)-...-\dfrac{1}{50}\left(1+2+3+...+50\right)\)

\(=\dfrac{-1}{3}\cdot\dfrac{3\cdot4}{2}-\dfrac{1}{4}\cdot\dfrac{4\cdot5}{2}-...-\dfrac{1}{50}\cdot\dfrac{50\cdot51}{2}\)

\(=\dfrac{-4}{2}-\dfrac{5}{2}-...-\dfrac{51}{2}\)

\(=\dfrac{-\left(4+5+...+51\right)}{2}\)

\(=\dfrac{-\left(51+4\right)\cdot\dfrac{48}{2}}{2}=-\dfrac{1320}{2}=-660\)

Đặt \(S=\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+.....+99}+\frac{1}{50}\)

Đặt E = \(\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+....+99}\)

\(E=\frac{1}{2.3:2}+\frac{1}{3.4:2}+....+\frac{1}{99.100:2}\)

\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

E = 49/100 : 1/2 = 49/50

Vậy \(S=\frac{49}{50}+\frac{1}{50}=\frac{50}{50}=1\)

cách tính như thế nào bạn?????

Ahhh...trình bày dài lắm,cách làm thôi nhé

bạn vào nick ''nguyen thi thanh loan'' nhé

Là sao vậy

=2/6+2/12+....+2/51.50 

=2(1/2.3+1/3.4+...+1/51.50)

=2(1/2 - 1/3 + ....... + 1/50 -1/51)

=2(1/2-1/51)

=2.49/102=49/51

học tốt

\(P=1+\frac{1}{1+2}+\frac{1}{1+2+3}+........+\frac{1}{1+2+3+.......+50}=1+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+......+\frac{1}{\frac{50.51}{2}}=1+\frac{2}{2.3}+\frac{2}{3.4}+......+\frac{2}{50.51}=1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{50.51}\right)\) \(Taco:\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\)

\(\Rightarrow P=1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-.......+\frac{1}{50}-\frac{1}{51}\right)=1+2\left(\frac{1}{2}-\frac{1}{51}\right)=1+1-\frac{2}{51}=2-\frac{2}{51}=\frac{100}{51}\)

Bằng \(\frac{100}{51}\)

#)Giải :

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

\(\Rightarrow A=\frac{1}{2.3:2}+\frac{1}{3.4:2}+\frac{1}{4.5:2}+...+\frac{1}{50.50:2}\)

\(\Rightarrow A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{100.101}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{51}\)

\(\Rightarrow\frac{1}{2}A=\frac{49}{102}\)

\(\Rightarrow A=\frac{49}{102}.\frac{1}{2}\)

\(\Rightarrow A=\frac{49}{204}\)

là 6375

hãy k nếu bạn thấy đây là câu tl đúng :)

chúc bạn hok tốt :P

1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 +...+ 50+50+50+50

= 1x5 + 2x5 + 3x5 +...+50x5

=5x(1+2+3+...+50)

=5x1275

=6375

6375 bạn nha

ai thấy đúng thì tk mình nha 

gửi kết bạn luôn nha

ai hâm mộ kudo shinichi , kaito kid , ran ,..... nói chung là tất cả cái gì tới liên quan tới thám tử lừng danh conan

kết bạn nha gửi lời mời cho mình mình luôn luôn tk đồng ý