UC知道1×2×1/3 +2×3×1/4+………+98×99×1/100=?
来源：百度知道 编辑：UC知道 时间：2024/05/14 11:14:42
这道题小弟不会做，还请各位高手们赐教，小弟感激不尽，有急用，多谢。
看不出来规律啊..
要拿极限做
通式是 (X-1)X/(X+1)
LIM (X-1)X/(X+1)=X-2
就是说约等于算(1-2)+(2-2)+(3-2)+(4-2)....+(100-2)
结果是4850
an=n-1+2/(n+2) (n=1 ~ 98)
估计没有简便方法，用MATLAB解，代码如下：
symsum(k*(k+1)/(k+2),k,1,98)
ans =
6637902283102205681790933366897772969343711/1394407504594249543290676178706246071136
表示成小数，保留1000位有效数字如下：
s=vpa(ans,1000)
s =
4760.374755035279240521610235351316506315817944253416903306353067913174439115065100993211375537846240827105902745800161918971528669804007718502569094958799212977355438712875402068702835003256007224267627872680672207943405163007712184595218515517049804840315729082468276673218379741205518145070090251658976150557334791807894294187558110199433278181691616324455126098025940381638274476675523013586889651843997157365643256028197695130234973553337032152946085943396662010412693340201681132726148129334087344165595010065815728189115990444634492399630515740421363614656238344634206455632723049148661791396164