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Từ dãy trên ta có:
(\(\frac{3}{2}\)+\(\frac{1}{2}\))+(\(\frac{8}{3}\)+\(\frac{2}{3}\))+......+(\(\frac{2600}{51}\)+\(\frac{1}{51}\)) < vì không có cách nhập hỗn số nên mình đổi ra phân số >
= 2 + 3 + 4 + 5 + 6 + ..........................+ 51
Từ 2 -> 51 có :( 51 - 2 ) : 1 + 1 = 50 số
Chia ra : 50 : 2 = 25 cặp
ta có( 51 + 2 ) x 25 =1325
Vậy tổng trên có kết quả bằng 1325 (tớ chỉ nghĩ thế thôi chứ sai đừng trách nhá.Đùa thôi,đúng đấy )
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\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+50}\)
\(=\frac{1}{2\times\left(2+1\right):2}+\frac{1}{3\times\left(3+1\right):2}+\frac{1}{4\times\left(4+1\right):2}+...+\frac{1}{50\times\left(50+1\right):2}\)
\(=\frac{1}{2}\times\frac{1}{2\times3}+\frac{1}{2}\times\frac{1}{3\times4}+\frac{1}{2}\times\frac{1}{4\times5}+...+\frac{1}{2}\times\frac{1}{49\times50}\)
\(=\frac{1}{2}\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{49\times50}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{50}\right)=\frac{1}{2}\times\frac{12}{25}=\frac{6}{25}\)
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+..+50}\)
\(=\frac{1}{2.\left(2+1\right):2}+\frac{1}{3.\left(3+1\right):2}+\frac{1}{4.\left(4+1\right):2}+..+\frac{1}{50.\left(50+1\right):2}\)
\(=\frac{1}{2}.\frac{1}{2.3}+\frac{1}{2}.\frac{1}{3.4}+\frac{1}{2}.\frac{1}{4.5}+..+\frac{1}{2}.\frac{1}{49.50}\)
\(=\frac{1}{2}.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+..+\frac{1}{49.50}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{50}\right)=\frac{1}{2}.\frac{12}{25}=\frac{6}{25}\)
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\(=\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{50\cdot\dfrac{49}{2}}\)
\(=\dfrac{1}{2\cdot\dfrac{3}{2}}+\dfrac{1}{3\cdot\dfrac{4}{2}}+...+\dfrac{1}{50\cdot\dfrac{49}{2}}\)
\(=\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+...+\dfrac{2}{49\cdot50}\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)
=2*24/50=48/50=24/25
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A = 1 × 2 × 3 + 2 × 3 × 4 + .....+ 48 × 49 × 50
ta có 4 x A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x (5 -1) + .....+ 48 × 49 × 50 x (51 - 47)
= 1 x 2 x 3 x 4 + 2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + ... + 48 x 49 x 50 x 51 - 47 x 48 x 49 x 50
= 48 x 49 x 50 x 51
suy ra A = (48 x 49 x 50 x 51) : 4
= 12 x 49 x 50 x 51
nhớ k cho mik nha rùi mik lm nốt cho
Ta có: \(\left(1-\frac{1}{2^2}\right)\times\left(1-\frac{1}{3^2}\right)\times\left(1-\frac{1}{4^2}\right)\times...\times\left(1-\frac{1}{50^2}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{2499}{2500}\)
\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{49.51}{50.50}\)
\(=\frac{1.2.3.....49}{2.3.4.....50}\times\frac{3.4.5.....51}{2.3.4.....50}\)
\(=\frac{1}{50}\times\frac{51}{2}\)
\(=\frac{51}{100}\)