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.
If I remember correctly it should be B because every input has to have 1 output. I apologize if it’s wrong ( I haven’t had those problems since 8th grade I’m currently in 10th)
1:3 :) why? well if we think about it 2:9 is just not gonna work, cross that out. 3:18? no, thanks. 1:3 is it
Answer: $12,697.80
Step-by-step explanation:
To find 15% of $84,652, you want to multiply them together.
0.15×84,652=12,697.80
Now, we know that $12,697.80 is 15% of $84,652.