Question

1/1*4+1/4*7+1/7*10+....+1/97*100 怎么算

就这道题 用简便运算 或脱式计算 急急急~~！！~~

Answer 1

这题有规律的：
1/n*(n+3)=1/3 *[1/n-1/(n+3)]
所以:
1/1*4=(1/3)*[1-1/4]
1/4*7=(1/3)*[1/4-1/7]
1/7*10=(1/3)*[1/7-1/10]
....
1/97*100=(1/3)*[1/97-1/100]
看出规律没 1/4 1/7 ...都可以消去

所以呢：
1/1*4+1/4*7+1/7*10+....+1/97*100
=(1/3)[1-1/100]
=33/100

Answer 2

1/1*4+1/4*7+1/7*10+....+1/97*100
=1/3*[(1-1/4)+(1/4-1/7)+....+(1/97-1/100)]
=1/3*(1-1/100)
=33/100

Answer 3

1/1*4+1/4*7+1/7*10+....+1/97*100

=1/3 * (1/1-1/4+1/4-1/7+...+1/97-1/100)

=1/3 * (1/1-1/100)

=1/3 * 99/100

=33/100

Answer 4

1/n*(n+3)=1/3 *[1/n-1/(n+3)]
原式=1/3-1/300=33/100

Answer 5

33/100