Prove recursive series is decreasing

[jaunty coral]

how do i prove this, im rly bad at proving
im gonna be inactive

[jaunty coral]

the limit is pretty obvious but how do i prove its decreasing again?? havent done these stuff for a while

[tribal hull]

You can show it's decreasing by induction @jaunty coral

[quiet dirge]

induction

[jaunty coral]

oh i completely forgot

[golden meadow]

.solved