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.
In km/min it is 0.2km/min while on converting into m/sec..it is 3.33 m/sec........
Answer:
5.917
Step-by-step explanation:
Each child has a 50% chance to be a girl and 50%chance to be a boy so with 4 children the probability is
Answer:
$1,665.19
Step-by-step explanation:
Interest=PRT/100 where P is the principal amount deposited by Michelle, R is the rate offered per year in terms of percentage, T is the period in years
Substituting P for $1385, T for 7 years, R for 2.89% we obtain interest as follows
Interest=$1,385*2.89*7 years/100=$280.1855
Balance after 7 years will be the sum of principal amount and interest gained
Balance=$1,385+$280.1855
=$1,665.1855
Rounding off to 2 decimal places
Balance=$1665.19
Therefore, Michelle's balance is $1,665.19