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Cryptokyo TMUA Problem Set · Q16

Functions & graphsPowers & logarithms

Find the value of

log⁡(12)+log⁡(43)+log⁡(94)+log⁡(165)+⋯+log⁡(n2n+1)\log\left(\frac12\right)+\log\left(\frac43\right)+\log\left(\frac94\right)+\log\left(\frac{16}5\right)+\cdots+\log\left(\frac{n^2}{n+1}\right)

in the form log⁡f(n)\log f(n) where f(n)f(n) is some function of nn.

Alog⁡(n!n+1)\log\left(\frac{n!}{n+1}\right)
Blog⁡(n2n+1)\log\left(\frac{n^2}{n+1}\right)
Clog⁡(n!(n+1)!)\log\left(\frac{n!}{(n+1)!}\right)
Dlog⁡((n!)2n+1)\log\left(\frac{(n!)^2}{n+1}\right)
Elog⁡((n+1)!n!)\log\left(\frac{(n+1)!}{n!}\right)

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