Carcass wrote:
If k is the sum of the reciprocals of the consecutive integers from 41 to 60 inclusive, which of the following are less than k?
Indicate
all such statements.
❑
14❑
13❑
12Approximation works to solve this question.
We know that:
140>141,142,....,149And:
150>151,152,....,159So we can approximate
k:
k=141+142+...+151+152+....+160k<140+140+....+150+150+....+160There are 9 numbers between 41 and 49, and ten between 50 and 59, with the lone 60 at the end, so:
k<9∗140+10∗150+160This simplifies to:
k<940+1050+160k<940+15+160940 is slightly less than
1040 or
14, and
160 is less than
150, so essentially what we have is:
k<14+15+150k<0.25+0.2+0.02k<0.47Giving us the answers A and B