Gear problem

[CokeandIron]

I can't get my chain to shift to the smallest gear wheel at the rear.
Does the cable just want tensioning and if so where do I do it.
If the cable has stretched,do I need to pull the slack through after slackening the screw before fine tuning the adjustment.

[X-RAY]

since adjusting the cable is a pain, and scary for some, i always check the limit screws first. and if you have to mess with the cables, i find it easier to undo it and start from scratch rather than trying to move it a little at a time from where its at now. i dont think older cables stretch much, either. new ones do, then i believe they stay the same until they break.

[cyclerUK]

Make sure there is a small amount of slack in the cable.
This should allow the chain to move to the small sprocket.
Then re-adjust to get the rest right.
Check out Alex's video:-
http://bikeride.com/adjust-rear-derailleur/

try moving the derailleur by hand to see if that helps.