I will try and help you restore your iPhone to iOS 11.1.1 after a failed software update. To fix this, you need to enter DFU Mode (Device Firmware Update Mode) this will reinstall the iOS version, even if it is beyond repair. To enter DFU Recovery Mode, follow these steps:
Once you are in DFU mode, your screen will be black, so don't interact with the device at all. iTunes will prompt you that a device is in DFU mode, once it is connected, click on "Restore iPhone", iTunes may need to download iOS 11.1.1 from the iPhone Software Update Server, which is around 3GB, so be patient.
Don't disconnect the device during the restore process, a video link is here: https://www.youtube.com/watch?v=KbLaxZzb3Iw
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