Question

数列的前n项和~~~~~~~~~~~orz

Answer 1

Tn=p+2P^2+3p^3+...+np^n

=p(1+p+p^2+...+p^(n-1))+p^2(1+p+p^2+...+p^(n-2))+p^3(1+p+p^2+...+p^(n-3))+...+p^(n-1)(1+p)+p^n(1)

=p(p^n-1)/(p-1)+p^2[p^(n-1)-1]/(p-1)+...+p^(n-1)(p^2-1)/(p-1)+p^n(p-1)/(p-1)

=[p^(n+1)-p+p^(n+1)-p^2+p^(n+1)-p^3+...+p^(n+1)-p^n]/(p-1)

=[np^(n+1)-p(1+p+p^2+...+p^(n-1))]/(p-1)

=[np^(n+1)-p(p^n-1)/(p-1)]/(p-1)

=np^(n+1)/(p-1)-p(p^n-1)/(p-1)^2