(a1,a2,.....a4....)is progression where an=n^2/n^3+200 the largest term of progression
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Therefore the largest term of progression would be 7.
Given : a₁, a₂, a₃, a₄ ..... is progression where
To find : The largest term of the progression.
solution : here
differentiating w.r.t n we get,
using the quotient rule,
so,
here at we get, n = 0, 400⅓
again differentiating w.r.t n we get,
at n = 0, we get > 0 means at n = 0 will be minimum.
at n = 400⅓ we get < 0
means at n = 400⅓ will be maximum.
so the largest term of progression n = 400⅓ ≈ 7
Therefore the largest term of progression would be 7.
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