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question mark

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

Tushar Watts , 15 Years ago
Grade 12
anser 1 Answers
Ramesh V

Last Activity: 15 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

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