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if ∑ I(r) =n(2n^2 +9n +13) (limit from r=1 to n) then find sum of ∑ root of I(r).

if ∑ I(r) =n(2n^2 +9n +13) (limit from r=1 to n) then find sum of ∑ root of I(r).

Grade:12

1 Answers

Akshay
185 Points
7 years ago
∑k2 = [2n+ 3n2+n]/6  call it eq.(1)
∑k = [n2+n]/2 call it eq.(2)
∑1 = n call it equation (3)

Note all limits are 1 to n.
6*eq(1) + 12*eq(2) + 6*eq(3) will give you,

∑6*(k2+2k+1)= 2n3+9n2+13n,

So, l(k) = 6*(k+1)2,
root[l(k)] = root(6) * (k+1).
just use equation 2 and 3 to solve for ∑root(l(k))

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