Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

Let S_n= _ r=1 ^n 6 r+9 (r+1)^2(r+2)^2 . If S_ = p q where p, q N , then find the least value of |p-q| .

Correct answer

Step-by-step solution

aligned S_n & = _ r=1 ^n 6 r+9 (r+1)^2(r+2)^2 = _ r=1 ^n 3(2 r+3) (r+1)^2(r+2)^2 =3 _ r=1 ^n ( 1 (r+1)^2 - 1 (r+2)^2 ) S_n & =3 ( 1 4 - 1 9 + 1 9 - 1 16 + + 1 (n+2)^2 )=3 ( 1 4 - 1 (n+2)^2 ) _ n S_n & = 3 4 p q |p-q|_ least =1 aligned

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