summation of k^5 for first n natural no.s

$$(k+1)^6=k^6+6k^5+15k^4+20k^3+15k^2+6k+1$$

then you summed up for k from 1 to n
and you Reduced certain terms
and you got
(n+1)^6=1+6S_5+15S_4+20S_3+15S_2+6S_1+n

$$<br /> how did you get $$

(n+1)^6 on lhs...and summation of k^6 on rhs as 1..cud you give steps...rest all the terms are ok on rhs...shouldnt we get an S6 on rhs from the first term....
i would be thankful to you if you cud give the finl result too if possible.....or a source where it wud be present.....as i am more interested in the reswult rather than its derivation and method of getting it.....the result of summation of k^5 is of utmost importance to me now...
THANK YOU for answering me!!

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