Problem 47 (difficulty: 5/10)

Express the following sums in closed forms!

 (1)  \(\displaystyle 1+3+5+7 +\ldots + (2n+1);\)    
 (2)  \(\displaystyle \displaystyle \frac{1}{1\cdot 2\cdot 3} +\ldots +\frac{1}{n\cdot (n+1) \cdot (n+2)} ;\)
 (3)  \(\displaystyle 1\cdot 2 + \ldots +n\cdot (n+1);\)    
 (4)  \(\displaystyle 1\cdot 2\cdot 3+\ldots + n\cdot (n+1)\cdot (n+2).\)

Give me another random problem!