Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. calculus
  3. use the principle of mathematical induction to sho

Use the Principle of Mathematical Induction to show that the following statement is true for...

70.2K

Verified Solution

Question

Calculus

image

Use the Principle of Mathematical Induction to show that the following statement is true for all natural numbers n.19+8+7+...+(10-n) = n(19-n)What two conditions must the given statement satisfy to prove that it is true for all natural numbers? Select all that apply.The statement is true for the natural number 1.The statement is true for any two natural numbers k and k + 1.If the statement is true for the natural number 1, it is also true for the next natural number 2.If the statement is true for some natural number k, it is also true for the next natural number k +1.***Show that the first of these conditions is satisfied by evaluating the left and right sides of the given statement for the first natural number.19+8+7+...+(10-n) = 2nn(19-n)9 = 9 (Simplify your answers.)To show that the second condition is satisfied, write the given statement for k+ 1.9+8+7++ (10-k) +(Use integers or fractions for any numbers in the expression. Type your answer in factored form.)

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

The following indicates the number of hours that Johnny spent studying the week before each exam...

Statistics
Q

A "leitmotif," developed and expanded by Richard Wagner, is a distinct snatch of music thatA....

Biology
Q

Capacitance of a sphere A is 4 F while for another sphere B it is...

Physics
Q

A uniform rod of length 7 is pivoted at point A it is struck by...

Physics
Q

In the figure below I m Find x 55 60

Basic Math
Q

Evaluate 1x 31 6 dx using the following graph 7 O S 3 6 dx...

Calculus
Q

Prove the identity 1 sin 2x sin 2x sec x csc x

Calculus
Q

help solve Product Cost Method of Product Costing Voice Com, Inc,...

Accounting
Q

It looks like a four-door SUV, drives like a four-door SUV but isnt. What is...

Accounting
Q

Prepare journal entries to record each transaction. 19 Jun: Sold a $2,500 watch on account,...

Accounting
Q

Motel Corporation is analyzing a capital expenditure that will involve a cash outlay of $134,200....

Accounting
Q

In an NOL carryback year, the NOL is combined with the AGI from the return...

Accounting