The difference between the sum of the first k terms of the series `1^3+2^3+3^3+....+n^3` and the sum of the first k terms of `1+2+3+.....+n` is `1980` . The value of k is :

Answer

9

Explanation

`[(k(k+1))/2]^(2)-(k(k+1))/2=1980`
or `(k(k+1))/2[(k(k+1))/2-1]`=1980
or `k(k+1)(k^(2)+k-2)=1980xx4`
or `(k-1)k(k+1)(k+2)=8xx9xx10xx11`
`thereforek-1=8rArrk=9`