Guest

If n is an odd integergreater than or equal to 1 , then show that the value of n 3 - (n-1 ) 3 + (n-2) 3 - ............+ (-1) n-1 . 1 3 is (n+1) 2 (2n-1) / 4

If n is an odd integergreater than or equal to 1 , then show that the value of


n3  - (n-1 ) 3 + (n-2)3  -  ............+ (-1) n-1 . 1 3 is


(n+1)2 (2n-1) / 4

Grade:12

1 Answers

Ramesh V
70 Points
12 years ago

n3  - (n-1 )3 + (n-2)3  -  ............+ (-1)n-1.13

2* [ n3  + (n-2)3  + (n-4)3  ............+ 23 ] - [ n3  + (n-1 )3 + (n-2)3  +  ............+ 23 + 13 ]

2*23* [ ((n-1)/2)3  + ((n-4)/2)3  ............+ 13 ] - [ n3  + (n-1 )3 + (n-2)3  +  ............+ 23 + 13 ]

sum of cubic terms of first n natural no's is:  n2(n+1)2/4

so, 16*(n-1)2(n+1)2/64 - n2(n+1)2/4

(2n-1)(n+1)2 / 4

hence solved

----

Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best.

Regards,
Naga Ramesh
IIT Kgp - 2005 batch

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free