Sum of infinite series 1/9+1/18+1/30+1/45+1/63...

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9 18 30 45 t(n)=an^2+bn+c 9 12 15 9=a+b+c ; 18=4a+2b+c; 3 3 30=9a+3b+ca=3/2,b=9/2,c=3 for ques t(n)=2/3(1/(n+1)(n+2)sum(1 - infinity)= 2/3 (1/n+1 - 1/n+2 )=2/3 (1/2) =1/3