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3 years ago

14

500 divides 25 is equal ?

1 answer:

Lelu [443]3 years ago

3 0

500 divides 25 is equal 20

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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =

Masteriza [31]

Complete Question

Find a formula for the sum of n terms. $\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

Use the formula to find the limit as $n \to \infty$

Answer:

$K_n = \frac{n + 73 }{n}$

$\lim_{n \to \infty} K_n = 1$

Step-by-step explanation:

So let assume that

$K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

=> $K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )$

=> $K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

Generally

$\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)$

So

$\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)$

$\sum\limits_{i=1}^n (8) = 36$

$K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

and

$\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)$

Therefore

$K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )$

$K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )$

$K_n = \frac{72}{n} + 1 + \frac{1}{n}$

$K_n = \frac{72 + 1 + n }{n}$

$K_n = \frac{n + 73 }{n}$

Now $\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0$

Therefore

$\lim_{n \to \infty} K_n = 1$

5 0

3 years ago

What is the value of 4p4

Paraphin [41]

Answer:

4P4 means the number of ways (permutations) of arranging 4 items from a collection of 4 items.

Step-by-step explanation:

8 0

3 years ago

Pls help choose 2 equations !! :) I will mark brainlist

SCORPION-xisa [38]

Answer:

C and E for sure

Step-by-step explanation:

6 0

3 years ago

Help me with it plizz

Liono4ka [1.6K]

2x + 9 = -65
2x = -65 - 9
2x = -74
x = -74/2
x = -37

So, your final answer is -37

Hope this helps!

3 0

2 years ago

the lenths of the sides of a triangle are in the extended ratio 5:9:10. the perimeter of the triangle is 48 cm. what are the len

dezoksy [38]

Answer:

What's my age im 1300

Step-by-step explanation:

3 0

3 years ago

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