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The firmware/software of your iPhone has been corrupted during the update. Your only option is force-restore the iPhone to factory settings through iTunes by putting it to recovery mode, which will erase everything from it.
But if you've backed up your iPhone to iTunes on your computer or iCloud, then you can restore all your data back after restoring your iPhone from iTunes/iCloud. You can also redownload all your past purchases for free using the same account.
Follow the steps below to restore your iPhone by putting it to recovery mode.
First download and install latest iTunes on your computer from here : https://www.apple.com/itunes/download/
Then connect the iPhone to your computer with the USB Cable.
Open iTunes application on your computer.
On your iPhone press and hold the Home button and the Power button at the same time for 10 seconds or until your iTunes shows a message telling you that it has detected an iPhone in recovery mode.
Click Restore or Restore and Update button.
Note : Put it to recovery mode while connected to computer and also in recovery mode your iPhone will show USB cable pointing to iTunes logo. And it will take a while to restore it.
Please let me know if that didn't work, so I will continue to help you until we fix the problem.
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