1+2P+3P^2 +4P^3 +5P^4 +……..+KP^K-1

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1+2P+3P^2+4P^3+5P^4+……..+KP^K-11+2P+3P^2+4P^3+5P^4+……..+KP^K-11+2P+3P^2+4P^3+5P^4+……..+KP^K-1S=1+2P+

1+2P+3P^2 +4P^3 +5P^4 +……..+KP^K-1
1+2P+3P^2 +4P^3 +5P^4 +……..+KP^K-1

1+2P+3P^2 +4P^3 +5P^4 +……..+KP^K-1
S=1+2P+3P^2 +4P^3 +5P^4 +……..+KP^K-1①
pS= P+2P^2+3P^3+4P^4+.+(k-1)P^K-1+KP^K②
①-②:
(1-P)S=1+P+P^2+P^3+...+P^K-1-KP^K
=(1-p^K-1)/(1-P)-KP^K
S=(1-p^K-1)/(1-P)^2-KP^K/(1-P)
不化简了.打得好累.