Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)快1小时内!

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Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)快1小时内!Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)快1小时内!Cn=1/(2(n^2)+2n)

Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)快1小时内!
Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)
快1小时内!

Cn=1/(2(n^2)+2n)求lim(C1+C2+C3+……+Cn)快1小时内!
Cn=1/2*1/n(n+1)
=1/2*[1/n-1/(n+1)]
所以原式=1/2[1-1/2+1/2-1/3+……+1/n-1/(n+1)]
=1/2*[1-1/(n+1)
=1/2*n/(n+1)
上下除以n
=1/2*[1/(1+1/n)]
所以极限=1/2*1/(1+0)=1/2

Cn=1/(2(n^2)+2n)=(1/2)[1/n-1/(n+1)]
C1+C2+C3+……+Cn=(1/2)[1-1/(n+1)]=(1/2)*n/(n+1)
lim(C1+C2+C3+……+Cn)=1/2