Wednesday, May 29, 2019

elementary number theory - how can one find the value of the expression, (12+22+32+cdots+n2)











how can one find the value of the expression, (12+22+32++n2)



Let,



T2(n)=12+22+32++n2



T2(n)=(12+n2)+(22+(n1)2)+




T2(n)=((n+1)22(1)(n))+((n+1)22(2)(n1))+


Answer



Hint: (n+1)3n3=3n2+3n+1 and use telescopic sum.


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