b1＝2 ，bn＋1（下角标）＝bn＋3n＋2，求｛bn｝通项公式

显示全部楼层 · 2012-1-6 13:20:59

bn=2n+3n(n+1)/2具体算法是：b1＝2
b2-b1=3+2
b3-b2=3×2+2……
bn-bn-1（下角标）=3×（n-1）+2等号左面相加得：bn=2n+3n(n+1)/2...

千问 · 2012-1-6 13:20:59

bn＋1-bn＝3n＋2.....b2-b1=3+2把这n项相加得bn+1=b1+2*n+3*n(n+1)/2=2(1+n)+3*n(n+1)/2=（n+1）(2+3n/2)=(n+1)(3n+4)/2...

千问 · 2012-1-6 13:20:59

bn+1 - bn = 3n + 2,bn - bn-1 = 3(n-1) + 2 ... b2 - b1 = 3*1 + 2全部相加：bn+1 - b1=3n(n+1)/2+2n所以：bn = 3n(n-1)/2 + 2n...