Question

[❖︵Ňɠυүễη Çɦâυ Ƭυấη Ƙїệт♔]

\(\text{Tìm x , biết : }\)

\(a.\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)

\(b.x-\left(\frac{50x}{100}+\frac{25x}{200}\right)=\frac{45}{4}\)

\(c.1+2+3+4+...+x=820\)

Ai làm nhanh mk cho 20 tích

Answer 1

[Huỳnh Quang Sang]

\(a)\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+...+\frac{1}{x(x+3)}=\frac{101}{1540}\)

\(\Rightarrow\frac{1}{3}\left[(\frac{1}{5}-\frac{1}{8})+(\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3})\right]=\frac{101}{1540}\)

\(\Rightarrow\frac{1}{3}\left[\frac{1}{5}-\frac{1}{x+3}\right]=\frac{101}{1540}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}:\frac{1}{3}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)

\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}=\frac{5}{1540}=\frac{1}{308}\)

\(\Rightarrow x+3=308\Rightarrow x=305\)

\(b)x-(\frac{50x}{100}-\frac{25x}{200})=\frac{45}{4}\)

\(\Rightarrow x-(\frac{100x}{200}-\frac{25x}{200})=\frac{45}{4}\)

\(\Rightarrow x-\frac{5x}{8}=\frac{45}{4}\)

\(\Rightarrow\frac{3x}{8}=\frac{45}{4}\)

\(\Rightarrow3x=\frac{45}{4}\cdot8\)

\(\Rightarrow3x=90\Rightarrow x=30\)

\(c)1+2+3+4+...+x=820\)

Ta có : \(1+2+3+4+...+x=\frac{(1+x)\cdot x}{2}\)

Do đó : \(\frac{(1+x)\cdot x}{2}=820\)

\(\Rightarrow(1+x)\cdot x=820\cdot2\)

\(\Rightarrow(1+x)\cdot x=1640\)

\(\Rightarrow(1+x)\cdot x=40\cdot41\)

Vì x và x + 1 là hai số tự nhiên liên tiếp nên => x = 40

Chúc bạn học tốt :3