Question

数列求an

已知数列a(n+1)=(n+2/n)an 且a1=1 求an 注 等号左边n+1 是an的后一项

Answer 1

a2=(3/1)*a1
a3=(4/2)*a2
a4=(5/3)*a3
a5=(6/4)*a4

an=((n+1)/(n-1))*a(n-1)
上面n-1个等式相乘 化简得
an=((3/1)*(4/2)*5/3* *(n+1)/(n-1))*a1
=n*(n+1)/2

Answer 2

a2=3/1*a1
a3=4/2*a2
a4=5/3*a3
a5=6/4*a4
...

a2*a3*a4..*an=(a1*a2*..an-1)(3*4*5...n+1)/(1*2...*n-1)==(a1*a2*..an)n(n+1)/2
化简
an=a1*n(n+1)/2=n(n+1)/2