find the sum of squares of ‘n’ natural number (give brief ansanswer

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find the sum of squares of ‘n’ natural number (give brief ansanswer

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Sumof‘n’naturalnumbersLet the sum of the first

terms of AP :n,aa+,da+2d…The

th term for this AP isna+(n-1). LetdSdenote the sum of the firstterms of the AP . We havenS=a+(n-1)+d(a+2d)+ … +[a+(n-1)d]___ ( 1 )Rewriting the terms in reverse order , we have

S=[a+(n-1)d]+[a+(n-2)d]+ … +(a+d)+___ (2)aOn adding ( 1 ) & (2) term – wise . We get

2S## OR ,

2Sn[2a+(n-1)d]( since there areterms )n## OR ,

S=So ,

thesumofthefirstntermsofanAPisgivenbyS=Sumofsquaresof‘n‘naturalnumbersΣn²= [tex] \sf {\dfrac{[n(n+1)(2n+1)]}{6}} [/tex]