Inverse Trigonometric Functions

If \(\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\frac{1}{1+n(1+1)}\right]=\tan ^{-1}[x]\), then \(x\) is equal to