cho \(E=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+n}\right)\)và \(F=\frac{n+2}{n}\)với n thuộc N* . Tính \(\frac{E}{F}\)

Cho \(E=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+n}\right)\)

và \(F=\frac{n+2}{n}\)với \(n\in N^{\cdot}.\)Tính \(\frac{E}{F}\)

CMR \(\forall n\in\)N* ta có

\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+...+\left(\frac{1}{2n-1}-\frac{1}{2n}\right)=\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}\)

Thuc hien phep tinh

e)\(\left(\frac{2}{3}-\frac{-2}{7}-\frac{1}{14}\right):\left(-1-\frac{3}{7}+\frac{3}{28}\right)\)

f) \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)...\left(\frac{1}{100}-1\right)\)

Tính:

\(F=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right)...\left(\frac{1}{n^2}-1\right)\)

1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)

So sánh:

a) \(A=\frac{n}{n+1};B=\frac{n+2}{n+3}\left(n\inℕ\right)\)

b) \(A=\frac{n}{n+3};B=\frac{n-1}{n+4}\left(n\inℕ^∗\right)\)

c) \(A=\frac{n}{2n+1};B=\frac{3n+1}{6n+3}\left(n\inℕ\right)\)

Giúp mình nhé gấp lắm ai trả lời đầu tiên mình sẽ tick