几何级数和证明证明1*r^1+2*r^2+```+nr^n
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/11 17:27:49
![几何级数和证明证明1*r^1+2*r^2+```+nr^n](/uploads/image/z/11456261-53-1.jpg?t=%E5%87%A0%E4%BD%95%E7%BA%A7%E6%95%B0%E5%92%8C%E8%AF%81%E6%98%8E%E8%AF%81%E6%98%8E1%2Ar%5E1%2B2%2Ar%5E2%2B%60%60%60%2Bnr%5En)
x){ھީw-6uI=/7>!
vBBv^Q\MR>v=`<lȳ%yؤM\ VRU`V`SmhBZ] `=Et AtP\fmD-XT&d
]aR0V]n\.f$;ڞ}>{ =:tONA1 ΄dG_P׳S^k!-H*7L0F8qDG[$ف "\
几何级数和证明证明1*r^1+2*r^2+```+nr^n
几何级数和证明
证明1*r^1+2*r^2+```+nr^n
几何级数和证明证明1*r^1+2*r^2+```+nr^n
令Sn=1*r^1+2*r^2+```+nr^n ①
rSn=1*r^2+2*r^3+```+nr^(n+1)②
①-②得
(1-r)Sn=(r^1+r^2+...+r^n)-nr^(n+1)=r(1-r^n)/(1-r)-nr^(n+1)
Sn=r(1-r^n)/(1-r)^2-nr^(n+1)/(1-r)=(r-r^(n+1)-n(1-r)r^(n+1))/(1-r)^2
分母相同,看分子,r-r^(n+1)-nr^(n+1)+nr^(n+2)与r相比较
r-r^(n+1)-nr^(n+1)+nr^(n+2)=r-r^(n+1)【1+n(1-r)】,∵
0