Unfortunately the current research does not support doing 100 pushups and resting for a month. Current research shows that the best way to gain strength, mass and endurance is through a concept called "Progressive Overload."
Typically at a gym this would be very easy to track, you can bench 125 this week for 3x8 reps. Next week we are going to "progressively overload" the chest and add 10 pounds onto this weeks lift. By adding new weight the muscle has to adapt to the new demands of it and will grow as you sleep and recover over the week.
Using bodyweight exercise(if you can't go to the gym) is as easy as adding more weights at the gym, you simply have to get a little cleverer. For example, in calisthenics we call this a "Progression". Standard Back exercise is a Pull up. If we can't do a full pullup because our back isn't developed enough yet we can do whats called a "Regression". We will adjust the exercise in a way to unload the movement to train our muscles to do it and scale up over time. Now lets say that Pull ups are now easy for you and you can do 20 in a row. We need to make it harder. That is when you learn new exercises like the Archer Pull Up or Muscle Up to challenge us to greater levels.
Hope this helped!