Answer:
(a)
(b)
Step-by-step explanation:
<u>Question 1</u>
Given the geometric series
3+15+75+375+...
<u>Question 2</u>
Given the series:
For example, if you are asked to estimate the sum of 545 + 723, you have to round the two numbers to the hundreds, so 545 would equal 500 and 723 would equal 700
500 + 700 = 1200, which wud be the estimation f the sum
Base case (<em>n</em> = 1):
• On the left side: 1/(1×2) = 1/2
• On the right side: 1/(1 + 1) = 1/2
Induction hypothesis: Assume the statement is true for <em>n</em> = <em>k</em> ; that is,
1/(1×2) + 1/(2×3) + … + 1/(<em>k</em> × (<em>k</em> + 1))) = <em>k</em>/(<em>k</em> + 1)
Inductive step (<em>n</em> = <em>k</em> + 1):
1/(1×2) + 1/(2×3) + … + 1/(<em>k</em> × (<em>k</em> + 1))) + 1/((<em>k</em> + 1) × (<em>k</em> + 2)))
= <em>k</em>/(<em>k</em> + 1) + 1/((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> × (<em>k</em> + 2) + 1) / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> ² + 2<em>k</em> + 1) / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> + 1)² / ((<em>k</em> + 1) × (<em>k</em> + 2))
= (<em>k</em> + 1) / (<em>k</em> + 2)
and this is what we wanted to show.
The domain for the function f(x) = |x + 1| is the set of all real numbers.
The range of the function is the set of positive real numbers.
Given the function f(x) = |x + 1|
f(-4) = |-4 + 1| = | -3| = 3
This means that the number -4 is at a distance of 3 units away from -1 on the number line.
f(2) = |2 + 1| = |3| = 3
This means that the number 2 is at a distance of 3 units away from -1 on the number line.
f(1.5) = |1.5 + 1| = |2.5| = 2.5
This means that the number 1.5 is at a distance of 2.5 units away from -1 on the number line.
Learn more at:
Domain and range - brainly.com/question/2264373
Absolute value or modulus function - brainly.com/question/12980508
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