Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

OR

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

93219 24448 / 99871 78554

Mon to Sat - 10 AM to 7 PM

23. For which positive integers n is the ratio, sum k = 1 to n k ^ 2 an integer? sum k = 1 k (A) odd n only (B) even n only

Asked by rareaditi4159 29th September 2023, 8:25 PM
Answered by Expert
Answer:
It is understood we have to find the ratio of begin mathsize 14px style space fraction numerator begin display style sum from k equals 1 to n of end style space k squared over denominator begin display style sum from k equals 1 to n of end style space k end fraction end style
 
begin mathsize 14px style sum from k equals 1 to n of k squared space equals space fraction numerator n space left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction end style
 
 
begin mathsize 14px style sum from k equals 1 to n of k space equals space fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style
 
begin mathsize 14px style space fraction numerator begin display style sum from k equals 1 to n of end style space k squared over denominator begin display style sum from k equals 1 to n of end style space k end fraction space equals space fraction numerator left parenthesis 2 n plus 1 right parenthesis over denominator 3 end fraction end style
 
above ratio is integer when , n = 1 , 4, 7 , 10 , 13 ................
Answered by Expert 29th September 2023, 9:06 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp