ESP-01 ( ESP8266) with Arduino mega Problem.

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Hello,
I have been starting to learn Arduino since a few days ago. I need your help.
I tried to connect esp-01 using arduino mega 2560.
but there is no response from esp-01.

I just want to get a response "OK" from "AT" command in serial port program ( Putty).
Please give me a piece of advice.

Hardware connection

ESP-01

TX ------> Arduino mega RX1 (19 pin)
GND ----> GND from External Power Supply + Arduino mega GND
CH_PD ----> 3.3V from external Power Supply
GPIO2 -----> No connection
RST --------> 3.3V from external Power Supply
GPIO0 ------> No connection
VCC --------> 3.3V from external Power Supply
RX ----------> Arduino mega TX1 (18 pin) + Level shift circuit to get 3.3v from 5v of Arduino.

I confirmed COM Port ( COM3) and then run serial monitor of Arduino IDE.
I typed "AT" but there is no response. Could you let me know what problem is?

  1. Firmware update problem.

I also tried to update firmware to esp-01 using esp8266_flasher.exe tools
with hardware connection like below.

TX ------> Arduino mega RX1 (19 pin)
GND ----> GND from External Power Supply + Arduino mega GND
CH_PD ----> 3.3V from external Power Supply
GPIO2 -----> No connection
RST --------> 3.3V from external Power Supply

GPIO0 ------> GND

VCC --------> 3.3V from external Power Supply
RX ----------> Arduino mega TX1 (18 pin) + Level shift circuit to get 3.3v from 5v of Arduino TX1.

There is error message "Failed to connect". I have been doing it many times,but I could not do it.

I really appreciate your any comment.

Thanks.