Question

小学数学简便计算奥数题1×1/2+2×1/3+3×1/4+4×1/5……99×1/100

Answer 1

我只能帮你化下简：后面的自己看看能完成不
1×1/2+2×1/3+3×1/4+4×1/5……99×1/100
=1/2
+
2/3
+
3/4
+
4/5+.........99/100
=(1-1/2)X1+(1/2-1/6)X2+(1/3-1/12)X3+(1/4-1/20)X4............(1/99-1/9900)X99
=1-1/2X1+
1-1/6X2+
1-1/12X3+
1-1/20X4............
1-1/9900X99
=1-1/2
+
1-1/3
+
1-1/4+
1-1/5............
+1-1/100
=1+1+1+1..........1
-
(1/2+1/3+1/4+1/5+..........1/100)
=99-(1/2+1/3+1/4+1/5+..........1/100)
你自己再算(1/2+1/3+1/4+1/5+..........1/100)就OK了