This is a corollary to the other answers, just in case you're wondering why you can't use unbuffered RC sections.
An RC filter, by itself, is a 1st order system. When buffered 1st order stages are added (all the same, for simplicity), it is possible to make a filter whose transfer function is:
Suppose only two sections are considered. Then, the transfer function will be a 2nd order whose \$Q=0.5\$ and you will never be able to exceed it. For \$R=1,\;C=1\$:
For an unbuffered 2nd order filter, the transfer function will be (you can derive this however you wish):
Here \$Q=0.33\$ and it will never go above this. This is why your attempt at "gluing" RC sections would never be able to achieve an active filter's response -- it will never have a high enough \$Q\$. It's also the reason why you see the filters represented as triangles in the 1st picture: they are meant to be active filters. Also, there's a matter of gain, since your last picture shows a slight gain at the peak. You might be able to achieve peaking with RC filters, but its not a practical solution. A pure passive RC network will always have attenuation due to the finite impedances of the input and output.
Also, see @swineone's answer for a way to optimize the overall filter.