Pico infrared not transmitting correctly

This link might help. Note it uses a 0.9 duty cycle.

http://www.espruino.com/Pico+Infrared

Since you don't have a scope you might try this one liner to see the LED flashing.
analogWrite(A5,0.5,{freq:0.5});
It uses a lower frequency so you can see the flashes.

I did this one liner to flash the Green LED on a Pico. This is not PWM pin so you have to use the software PWM. PWM pins use the Timer peripherals built into the ARM chip.
analogWrite(B12,0.5,{freq:0.5,soft:true});