1.

Test the convergence of (a) [√n³+1 - √n³] (b): 1/n²log.logn​

Answer»

Step-by-step explanation:

hlo MATE here's your answer

SOLUTION

Note that:

You can only add inequalities when their signs are in the same DIRECTION:

If

and

(signs in same direction:

and

) -->

.

Example:

and

-->

.

You can only apply subtraction when their signs are in the opposite directions:

If

and

(signs in opposite direction:

and

) -->

(take the sign of the inequality you subtract from).

Example:

and

-->

.

Back to the original question:

If x + y + z > 0, is z > 1?

(1) z > x + y + 1 --> as the signs are in the same direction we can add two inequalities:

-->

-->

, so z may or may not be more than 1. Not sufficient.

(2) x + y + 1 < 0 --> as the signs are in the opposite direction we can subtract two inequalities:

-->

-->

. Sufficient.

i hope its help you mark as BRAINLIST and give thanks ok


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