两式相减是数学中一种重要的转化方法,很多数学问题,可借助于“两式相减”获得解决,应用十分广泛.那么怎样用“两式相减”呢?一、错项相减例1记数列{(2n+3)(1/2)~n}的前n项和为S_n,则S_n=.解∵a_n=(2n+3)(1/2)~n,∴有S_n=1/2·5+(1/2)~2·7+(1/2)~3·9+…+(1/2)~n(2n+3)1将1式两边乘以公比1/2,得 Two-type subtraction is an important mathematical transformation method, many mathematical problems can be resolved by means of “two-type subtraction ”, is widely used. So how to use (2n + 3) (1/2) ~ n} and S_n, then S_n =. Solution ∵a_n = (2n + 3) (1/2) ~ n, ∴ with S_n = 1/2 · 5 + (1/2) ~ 2 · 7 + (1/2) ~3 · 9 + ... + (1/2) ~n (2n + Formula multiplied by the ratio of 1/2 on both sides, too