Or at a pinch, take a single strand a bit thicker than the individual strands of the stranded wire, with plenty of extra length, and pinch the end of it against the insulation. Twist to lay it up smoothly with the stranded wire, then fold it sideways close to the tip of the stranded wire and tightly whip it round the stranded wire, in the direction that tightens the twist, back down towards the insulation. Take it under itself to make an overhand knot to secure it when you reach the insulation.
Don't tin a stranded wire to be inserted in a screw terminal block. The solder creeps under pressure, which causes the connection to become loose and intermittent. It is permissible to lightly tin the very tip to stop strands untwisting, but the part the screw bites on must not be tinned and must be free from solder wicking.
Don't try to put more than one solid wire (or two of the same diameter if there is a spring strip) under a single terminal's clamping screw. If you do, they will rock loose with the slightest movement.