等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 13:16:26
等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}假设n则Sm=

等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}
等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}

等差数列中前n项和为Sn若Sm等于n,Sn等于m求S{m+n}
假设n则Sm=Sn+(m-n)a1+(m-n)d
n=m+(m-n)a1+(m-n)d
a1+d=-1
S(m+n)=Sm+na1+nd=n+n*(-1)=0

Sm=m*(a1+am)÷2=m*[2a1+d(m-1)]÷2=n得2a1+d(m-1)=2n/m ①
Sn=n*[2a1+d(n-1)]/2=m得2a1+d(n-1)=2m/n ②
①-②:d(m-n)=(2n²-2m²)/mn
重点 mnd=﹣2(m+m)
S(m+n)=Sm+a1+md+a2+md+……+an+md
=Sm+Sn+mnd
=m+n+mnd
=﹣(m+n)