<s>[INST] Find the sum of binomial coefficients 
Calculate the value of the sum 
  $$
  \sum_{i = 1}^{100} i\binom{100}{i} = 1\binom{100}{1} + 
                                       2\binom{100}{2} + 
                                       3\binom{100}{3} + 
                                       \dotsb + 
                                       100\binom{100}{100}
$$

What I have tried: 
$$\begin{align}
  S &= 0\binom{100}{0}+1\binom{100}{1}+ \dotsb +99\binom{100}{99}+100\binom{100}{100} \\ \\
    &=100\binom{100}{100}+99\binom{100}{99}+ \dotsb +1\binom{100}{1}+0\binom{100}{0}
\end{align}$$
and I'm stuck here, I don't know if it's true or not, any help will be appreciated.
 [/INST] HINT :
Using$$\binom{n}{i}=\binom{n}{n-i}$$
just add the two sums you write to get $$2S=100\binom{100}{0}+100\binom{100}{1}+\cdots+100\binom{100}{99}+100\binom{100}{100}$$
</s>