problem indukcją:
\(\displaystyle{ \bigsum_{i=1}^{n}{i*2^i} = 2^{n+1}(n-1)+2}\)
\(\displaystyle{ \bigsum_{i=1}^{n+1}{i*2^i} = 2^{n+2}(n)+2}\)
\(\displaystyle{ \bigsum_{i=1}^{n+1}{i*2^i} - \bigsum_{i=1}^{n}{i*2^i} =}\)
\(\displaystyle{ =2^{n+2}n+2 - (2^{n+1}(n-1)+2)=2^{n+2}n+2 - 2^{n+1}(n-1)-2=}\)
\(\displaystyle{ =2^{n+2}n - 2^{n+1}(n-1)}\) i co z tym dalej zrobić?
