Can we prove these four binomial coefficient identities?

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By considering the expansion of \((1+x)^n\) where \(n\) is a positive integer, or otherwise, show that:

1. \(\dbinom{n}{0}+\dbinom{n}{1}+\dbinom{n}{2}+\dotsb+\dbinom{n}{n}=2^n\);

2. \(\dbinom{n}{1}+2\dbinom{n}{2}+3\dbinom{n}{3}+\dotsb+n\dbinom{n}{n}=n2^{n-1}\);

3. \(\dbinom{n}{0}+\dfrac{1}{2}\dbinom{n}{1}+\dfrac{1}{3}\dbinom{n}{2}+\dotsb+\dfrac{1}{n+1}\dbinom{n}{n}=\dfrac{1}{n+1}(2^{n+1}-1)\);

4. \(\dbinom{n}{1}+2^2\dbinom{n}{2}+3^2\dbinom{n}{3}+\dotsb+n^2\dbinom{n}{n}=n(n+1)2^{n-2}\).