SATHEE: Principle Of Mathematical Induction Question 47

Principle Of Mathematical Induction Question 47

Let $ S(k)=1+3+5…+(2k-1)=k^{2}. $ Then which of the following is true?

Options:

A) Principle of mathematical induction can be used to prove the formula

B) $ S(k)\Rightarrow S(k+1) $

C) $ S(k)\not{\Rightarrow }S(k+1) $

D) $ S(1) $ is correct

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ S(k)=1+3+5+…+(2k-1)=k^{2} $ $ S(1):1=1, $ which is true $ \because ,S(1) $ is true $ \therefore $ P.M.I cannot be applied Let S(k) be true, i.e, $ 1+3+5…+(2k-1)=k^{2}+1 $ $ \Rightarrow 1+3+5…+(2k-1)+2k+1 $ $ =k^{2}+2k+1+1=(k+1)^{2}+1 $ $ \therefore S(k)\Rightarrow S(k+1) $

BETA

sathee@iitk.ac.in

Media coverage of SATHEE

Play Store

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on I understand

Please select your preferred language
कृपया अपनी पसंदीदा भाषा चुनें

Principle Of Mathematical Induction Question 47

Let $ S(k)=1+3+5…+(2k-1)=k^{2}. $ Then which of the following is true?

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Video Solution

Menu