A= 44%
B= 42%

You add 26 and 40 to get 66 and divide by 150. you get .44. Multiply this by 100 and get 44% for A.

You add 40 and 23 to get 63 and divide by 150 again. you get .42. Multiply this by 100 and get 42% for B.

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3 years ago

Exercise 2.2.5. Let [[x]] be the greatest integer less than or equal to x. For example, [[π]] = 3 and [[3]] = 3. For each sequen

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Answer:

a) $\lim_{n\rightarrow \infty}a_n=0$

b) The limit is [[4/3]]=1, that is, $\lim_{n\rightarrow \infty}a_n=1$

Step-by-step explanation:

The definition of the limit of a sequence (an) is as follows:

$\lim_{n\rightarrow \infty}a_n=L$ (the sequence (an) converges to L) means that given $\epsilon>0$ , there exists some natural number N such that if n≥N, then $|a_n-L|$

We will use that [[x]] is a increasing function. That is, if x≤y then [[x]]≤[[y]]

a) For all $\epsilon>0$ , take N≥6. Then 1/N ≤1/6 and 5/N ≤ 5/6 < 1. We have that 0<5/N<1, therefore [[5/N]]=0 (0 is the biggest integer less than or equal than x, for any x on the interval 0<x<1)

For n≥N, we have that 1/n ≤ 1/N, hence 0< 5/n ≤ 5/N < 1 . As we discussed above, [[5/n]]=0. Then |a_n|=0, therefore $|a_n-0|=|a_n|=0$