数列bn满足b1=3/4,且3bn-bn-1=n,求bn
问题描述：
数列bn满足b1=3/4,且3bn-bn-1=n,求bn
注:bn-1是b(n一1)
答
原式→
3bn-(3/2)n=b(n-1)-(1/2)(n-1)-1/2
→
3bn-(3/2)n+3/4=b(n-1)-(1/2)(n-1)+1/4
令Tn=bn-(1/2)n+1/4
Tn=1/3T(n-1)
T1=1/2
Tn=1/2*3^(1-n)
bn=1/2*3^(1-n)+(1/2)n-1/43bn=b(n-1)+n3bn-(3/2)n=b(n-1)-(1/2)n3[bn-(1/2)n]=b(n-1)-1/2(n-1)-1/23[bn-(1/2)n]+3/4=b(n-1)-1/2(n-1)+1/43[bn-(1/2)n+1/4]=b(n-1)-1/2(n-1)+1/4换元即可