## CJam, <s>32</s> <s>30</s> <s>29</s> 28 bytes

    ri_"/\ /"2/f*)@,\f>+_z..e>N*

[Test it here.][1]

I was trying to help Reto golf his CJam answer but ended up with a solution that had nothing to do with his, so I figured I might as well post it myself.

### Explanation

This makes use of the symmetry of the output. In particular, the fact that the output is the same as its transpose.

First, we generate everything except the left edge:

    "/\ /"2/ e# Push an array with two strings: ["/\" " /"]
    ri       e# Read input and convert to integer N.
    f*       e# Repeat each of the two strings N times. That gives the first two rows.
    ~        e# Unwrap the array, dumping both arrays on the stack.
    {        e# While the top of the stack is truthy (non-empty)...
      _1>    e#   Copy the line and discard its first character.
    }h
    &        e# The last two lines are "/" and "". The second one isn't an issue but the first
             e# one is so we take the set intersection to combine them into a single "".
    ]        e# Wrap all lines in an array again.

Now we've got an array of strings representing the following grid:

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

The transpose of that has the necessary backslashes on the left edge, but lacks them at the top. We can now make use of [Dennis's rad tip](http://codegolf.stackexchange.com/a/52627/8478) to combine two ASCII grids into one, by taking the maximum of each corresponding pair of characters. The original and the transpose *only* differ in those positions where we need a backslash, and the other grid will have a space there. Hence the backslash will always be the maximum of the two characters:

    _z   e# Duplicate the grid and transpose it.
    ..e> e# For each pair of characters in corresponding positions, pick the maximum.
    N*   e# Join the lines by linefeed characters.

Due to the way `.` behaves for lists of different lengths, it would actually be enough to build up only the first half of the lines before this last step, but I haven't yet found a way to do so in fewer bytes.


 [1]: http://cjam.aditsu.net/#code=%22%2F%5C%20%2F%222%2Frif*~%7B_1%3E%7Dh%3B%3B%5D_z..e%3EN*&input=4