Statement-1: \[\sum\limits_{r=0}^{n}{{{\left( r+1 \right)}^{n}}{{C}_{r}}=\left( n+2 \right){{2}^{n-1}}}\]. |
Statement-2: \[\sum\limits_{r=0}^{n}{{{\left( r+1 \right)}^{n}}{{C}_{r}}{{x}^{r}}={{\left( 1+x \right)}^{n}}+nx{{\left( 1+x \right)}^{n-1}}}\]. |
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