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

Find the sum of n^th term of an series whose n^th term is given by n^2 (n^2-1).

Asked by nikhilrathour52 29th May 2019, 8:31 AM
Answered by Expert
Answer:
S u m space o f space n space t e r m s space o f space t h e space s e r i e s space w h o s e space n t h space t e r m space i s space n squared open parentheses n squared minus 1 close parentheses space i s space g i v e n space b y
equals sum from k equals 1 to n of k squared open parentheses k squared minus 1 close parentheses
equals sum from k equals 1 to n of open parentheses k to the power of 4 minus k squared close parentheses
equals sum from k equals 1 to n of k to the power of 4 minus sum from k equals 1 to n of k squared
equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses open parentheses 3 n squared plus 3 n minus 1 close parentheses over denominator 30 end fraction minus fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction
equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses open parentheses 3 n squared plus 3 n minus 1 close parentheses minus 5 n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 30 end fraction
equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses open square brackets 3 n squared plus 3 n minus 1 minus 5 close square brackets over denominator 30 end fraction
equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses open square brackets n squared plus n minus 2 close square brackets over denominator 30 end fraction
equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses open parentheses n plus 2 close parentheses left parenthesis n minus 1 right parenthesis over denominator 30 end fraction
equals fraction numerator n open parentheses n squared minus 1 close parentheses open parentheses n plus 2 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 30 end fraction
Answered by Expert 29th May 2019, 10:42 AM
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!

Free related questions

28th October 2021, 10:47 AM
29th October 2021, 8:01 AM
10th November 2021, 12:10 PM
10th November 2021, 12:10 PM

Chat with us on WhatsApp