Using binomial theorem, prove that `(101)^(50)> 100^(50)+99^(50)dot`

Explanation

To prove that \( 101^{50} > 100^{50} + 99^{50} \) using the Binomial Theorem, we can follow these steps:

### Step 1: Define the expressions
Let \( x = 101^{50} \) and \( y = 100^{50} + 99^{50} \). We need to show that \( x > y \), which is equivalent to proving that \( x - y > 0 \).

### Step 2: Write \( x - y \)
We have:
\[
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