Let a_{n} = \frac{1}{\left(log\right)_{n} 5} , \forall n \in N, n > 1, b = a24 + a25 and c = a2 + a3 + a4, then find (b

Engineering

Mathematics

base change theorem

Question

Let $a_{n} = \frac{1}{\log_{n} 5}, \forall n \in N$ , n > 1, b = a₂₄ + a₂₅ and c = a₂ + a₃ + a₄, then find (b – c).

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a_n = log₅n
$∴$ b = log₅24 +log₅25
and c = log₅2 + log₅3 + log₅4 = log₅24
$∴$ b – c = log₅25 = 2.