IPMAT IndoreAlgebra > Hard31323029✅ Correct Option: 1Related questions:IPMAT Indore 2023A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?IPMAT Indore 2023If f(n)=1+2+3+⋯+(n+1)f(n)= 1 + 2 + 3 +\cdots+(n+1) f(n)=1+2+3+⋯+(n+1) and g(n)=∑k=1k=n1f(k)g(n)= \sum_{k=1}^{k=n} \dfrac{1}{f(k)}g(n)=∑k=1k=nf(k)1, then the least value of nnn for which g(n)g(n)g(n) exceeds the value 99100\dfrac{99}{100}10099 is:IPMAT Indore 2025If the sum of the first 212121 terms of the sequence: lnab,lnabb,lnab2,lnab2b,…\ln \frac{a}{b}, \ln \frac{a}{b \sqrt{b}}, \ln \frac{a}{b^{2}}, \ln \frac{a}{b^{2} \sqrt{b}}, \ldotslnba,lnbba,lnb2a,lnb2ba,… is lnambn\ln \frac{a^{m}}{b^{n}}lnbnam, then the value of m+nm+nm+n is \qquad