一类数列的求和问题

The Summation of the First Species Sequence of Number

设{an}为等差数列,{bn}为等比数列,记αn=anbn,文中讨论了数列{αn}的有限项的求和问题;当{bn}满足一定条件时,{αn}的所有项的和的求解问题;设βn=a2nbn,当数列{βn}中的{bn}满足一定条件时,所有项的求和问题等.得到了一些结论,并给出了几个有关的例题.

Suppose { an } is an equal difference sequence of number, { bn } is an equal ratios sequence of numbe and an = a, bn, this thesis paper discusses the summation of finite terms in {an}. It also finds the solution to the summation of all terms in { an } when { bn } fulfils certain conditions. Suppose βn = an^2bn, it draws some conclusions on such problems as the summation of all terms and gives some related examples when { bn } in {βn} fulfils certain conditions.