数列一道错位相减的题求数列{n2的n次方}的前n项和Sn我这么做的.N=1时,SN=N(N+1)/2N不等于1时,SN=2+8+24+^+n*2^n2Sn= 4+8+……+2n*2^(n+1)然后怎么算n*2^nN乘以2的N次方
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![数列一道错位相减的题求数列{n2的n次方}的前n项和Sn我这么做的.N=1时,SN=N(N+1)/2N不等于1时,SN=2+8+24+^+n*2^n2Sn= 4+8+……+2n*2^(n+1)然后怎么算n*2^nN乘以2的N次方](/uploads/image/z/2180974-22-4.jpg?t=%E6%95%B0%E5%88%97%E4%B8%80%E9%81%93%E9%94%99%E4%BD%8D%E7%9B%B8%E5%87%8F%E7%9A%84%E9%A2%98%E6%B1%82%E6%95%B0%E5%88%97%7Bn2%E7%9A%84n%E6%AC%A1%E6%96%B9%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E6%88%91%E8%BF%99%E4%B9%88%E5%81%9A%E7%9A%84.N%3D1%E6%97%B6%2CSN%3DN%28N%2B1%29%2F2N%E4%B8%8D%E7%AD%89%E4%BA%8E1%E6%97%B6%2CSN%3D2%2B8%2B24%2B%5E%2Bn%2A2%5En2Sn%3D+4%2B8%2B%E2%80%A6%E2%80%A6%2B2n%2A2%5E%28n%2B1%29%E7%84%B6%E5%90%8E%E6%80%8E%E4%B9%88%E7%AE%97n%2A2%5EnN%E4%B9%98%E4%BB%A52%E7%9A%84N%E6%AC%A1%E6%96%B9)
数列一道错位相减的题求数列{n2的n次方}的前n项和Sn我这么做的.N=1时,SN=N(N+1)/2N不等于1时,SN=2+8+24+^+n*2^n2Sn= 4+8+……+2n*2^(n+1)然后怎么算n*2^nN乘以2的N次方
数列一道错位相减的题
求数列{n2的n次方}的前n项和Sn
我这么做的.
N=1时,SN=N(N+1)/2
N不等于1时,
SN=2+8+24+^+n*2^n
2Sn= 4+8+……+2n*2^(n+1)
然后怎么算
n*2^n
N乘以2的N次方
数列一道错位相减的题求数列{n2的n次方}的前n项和Sn我这么做的.N=1时,SN=N(N+1)/2N不等于1时,SN=2+8+24+^+n*2^n2Sn= 4+8+……+2n*2^(n+1)然后怎么算n*2^nN乘以2的N次方
a(n)=n*2^n,
S(n)=a(1)+a(2)+a(3)+...+a(n-1)+a(n)=1*2+2*2^2+3*2^3+...+(n-1)*2^(n-1)+n*2^n,
2S(n)=1*2^2+2*2^3+3*2^4+...+(n-1)*2^n+n*2^(n+1),
[到这里,你算的完全正确哈.接着,就开始错位相减了沙.]
S(n)=2S(n)-S(n)=n*2^(n+1)-1*2-1*2^2-1*2^3-...-1*2^n
=n*2^(n+1)-2[1+2+...+2^(n-1)]
=n*2^(n+1)-2[2^n-1]
n2的n次方什么意思?
SN=2+8+24+64+^+n*2^n
2*sn=4+16+48+...+(n-1)*2^n+n*2^(n+1)
两式相减得
sn=-2+(-4)+(-8)+(-16)+...+(-2^n)+n*2^(n+1)
=-2(2^n-1)+n*2^(n+1)
=(n-1)2^(n+1)+2