Question

Lim X tends to 1 ( 2018/1-x^2018 - 2019/1-x^2019)=? Whoever gonna solve it i will mark him brainlist.. ipromise​

Answer 1

Answer:

Use the property that

an - bn = (a - b)(an-1 + ban-2 + b2an-3 + ... + bn-2a + bn-1)

a = x

n = 2017

b = 1

x2017 - 1 = (x - 1)(x2016 + 1x2015 + 12x2014 + ... + 12015x + 12016

x2017 - 1 = (x - 1)(x2016 + x2015 + x2014 + ... + x + 1)

(x2017 - 1) / (x - 1) = [(x - 1) / (x -1)] (x2016 + x2015 + x2014 + ... + x + 1)

(x2017 - 1) / (x - 1) = (x2016 + x2015 + x2014 + ... + x + 1)

Now let x→1.

12016 = 12015 = 12014 = ... = 11 = 1

Note that the right hand side is just

1 + 1 + 1 + ... + 1 + 1 = 2017(1) = 2017

Then

liimx→1 [(x2017 - 1) / (x - 1)] = 2017

Answer 2

Answer:

an - bn = (a - b)(an-1 + ban-2 + b2an-3 + ... + bn-2a + bn-1)

a = x

n = 2017

b = 1

x2017 - 1 = (x - 1)(x2016 + 1x2015 + 12x2014 + ... + 12015x + 12016

x2017 - 1 = (x - 1)(x2016 + x2015 + x2014 + ... + x + 1)

(x2017 - 1) / (x - 1) = [(x - 1) / (x -1)] (x2016 + x2015 + x2014 + ... + x + 1)

(x2017 - 1) / (x - 1) = (x2016 + x2015 + x2014 + ... + x + 1)

Now let x→1.

12016 = 12015 = 12014 = ... = 11 = 1

Note that the right hand side is just

1 + 1 + 1 + ... + 1 + 1 = 2017(1) = 2017

Then

liimx→1 [(x2017 - 1) / (x - 1)] = 2017