#Java 7, <s>68</s> 65 bytes

    void c(int i){for(int x=0;x++<i;)System.out.print(i%2<1?92:'/');}

3 bytes saved thanks to *@user902383* and *@SeanBean*.

Just like [with this answer](http://codegolf.stackexchange.com/a/88656/52210), the shortest code-golf seems to loop and print. Both recursive and  
`void c(int i){System.out.print(new String(new char[i]).replace("\0",i%2<1?"\\":"/"));}`  
seems to be longer.

**Ungolfed & test code:**

[Try it here.](https://ideone.com/pTEWVZ)

    class M{
      static void c(int i){
        for(int x = 0; x++ < i;){
          System.out.print(i % 2 < 1
                            ? 92
                            : '/');
        }
      }
    
      public static void main(String[] a){
        for(int i = 0; i < 10; i++){
          c(i);
          System.out.println();
        }
      }
    }

**Output:**

    /
    \\
    ///
    \\\\
    /////
    \\\\\\
    ///////
    \\\\\\\\
    /////////