這很簡(jiǎn)單嘛,這是個(gè)等差乘等比的數(shù)列求和問(wèn)題,用錯(cuò)位相減法.
當(dāng)x=0時(shí)：S=0
當(dāng)x=1時(shí):S=100
當(dāng)x≠0,x≠1時(shí)
S=X+2X^2+3X^3+….+100X^100……………….1
XS=X^2+2x^3+….+99x^100+100x^101………….2
1-2得:
S(1-x)=x+x^2+x^3+…x^100-100x^101
根據(jù)等比數(shù)列求和公式：(x≠1且x≠0)
S(1-x)=((x(1-x^100))／(1-x))-100x^101
S=(x-101x^101+100x^102) ／((1-x)^2)