What is sqrt(n)-sqrt(n-1)<0.01 ?

The solution to sqrt(n)-sqrt(n-1) (1.00020001)/(0.0004)

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sqrt(n)-sqrt(n-1)<0.01

n - n - 1 < 0.01

n > \frac{1.00020001}{0.0004}

Interval Notation

(\frac{1.00020001}{0.0004}, \infty)

Decimal Notation

n > 2500.500025

Solution steps

n - n - 1 < 0.01

Add

n - 1

to both sides

n - n - 1 + n - 1 < 0.01 + n - 1

Simplify

n < 0.01 + n - 1

f (x) < g (x)

then

g (x) > 0

0.01 + n - 1 > 0 :

True for all

n

n < 0.01 + n - 1 : n > \frac{1.00020001}{0.0004}

Find singularity points

Find non-negative values for radicals:

n \geq 1

Combine the intervals

True for all n and n > \frac{1.00020001}{0.0004} and n \geq 1

Merge Overlapping Intervals

n > \frac{1.00020001}{0.0004}

Verify Solutions:

n > \frac{1.00020001}{0.0004}

True

The solution is

n > \frac{1.00020001}{0.0004}

\frac{∣ x + 2 ∣}{x} + \frac{x - 1}{x + 1} = 0

26 - \frac{5}{8} x = - \frac{5}{8} x + 26

4 x^{2} = 5 x

2 j^{2} - 3 j - 2

What is sqrt(n)-sqrt(n-1)<0.01 ?
The solution to sqrt(n)-sqrt(n-1)<0.01 is n>(1.00020001)/(0.0004)