Question

singma r =1 to 10 r×rpr. (plz answer it more clear​

Answer 1

${P}^{n}_n=\frac{n!}{(n-1)!}=n!\\\\so,{\sum}^{10}_{r=1} r{P}^{r}_r ={ \sum}^{10}_{r=1}r(r!)\\\\={ \sum}^{10}_{r=1}(r+1)r!-r!\\\\{ \sum}^{10}_{r=1}r{P}^{r}_r=2×1!-1!+3×2!-2!+\\4×3!-3!+....+11×10!-10!\\\\so,{\sum}^{10}_{r=1}r{P}^{r}_r=11×10!-1!=11!-1!$