Question

数列中的叠加法和叠乘法是怎么回事？请举个例子行吗，过程清楚，谢谢

Answer 1

叠加法：若a(n+1)-an=n,a1=1求an,
an=a1+(a2-a1)+(a3-a2)+...+(an-a(n-1))
=1+1+2+...+(n-1)=1+n(n-1)/2,
总结:若a(n+1)-an=bn,且bn前n项和可求,可用叠加法求an;
叠乘法:若a(n+1)/an=(n+1)/n,a1=1求an
an=a1×(a2/a1)×(a3/a2).×..×(an/a(n-1))
=1×(2/1)...×(n/(n-1))=n
总结:若a(n+1)/an=bn,且bn前n积和可求,可用叠乘法求an;