Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Live 1-1 coding classes to unleash the creator in your Child
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
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
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
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -