对于与自然数 n有关的一类求和恒等式f ( n) =g( n)的证明题 ,如果我们构造数列{an},其中 an =f ( n) - g( n) ,能证明 an+1-an =0 ,即 an+1=an,再验证 a1=0 ,那么立得an =0 ,从而有 f ( n) =g( n) .这种通过构造“零数列”来证题的方法 ,新颖别致、操作简便 ,现举例说明如下 . For the proposition of a kind of sum identities f(n) = g(n) related to the natural number n, if we construct the series {an}, where an = f( n) - g( n), we can prove an +1 -an =0, that is an+1=an, then verify that a1=0, then stand an =0, so that f(n)=g(n) . This method of constructing a “zero-numbered column” to test the question , New and unique, easy to operate, now illustrated as follows.