Question: Why is the recurrence relation of recursive factorial algorithm this?

```
T(n)=1 for n=0
T(n)=1+T(n-1) for n>0

```

Why is it not this?

```
T(n)=1 for n=0
T(n)=n*T(n-1) for n>0

```

Putting values of n i.e 1,2,3,4...... the second recurrence relation holds(The factorials are correctly calculated) not the first one.

Answer: 
This question is very confusing... You first formula is not factorial. It is simply T(n) = n + 1, for all n. Factorial of n is the product of the first n positive integers: factorial(1) = 1. factorial(n) = n \* factorial(n-1). Your second formula is essentially correct.
Where did you find the first one ? It's completely wrong.

It's only going to add 1 each time whatever the value is .