What is the sum, of 'n' terms in the series : log m + log -Maths 9th

What is the sum, of 'n' terms in the series : log m + log -Maths 9th
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(d) log \(\bigg[rac{m^{(1+n)}}{n^{(n-1)}}\bigg]^{rac{n}{2}}\) S = log m + log \(rac{m^2}{n}\) + log \(rac{m^3}{n^2}\) + ...........n terms= log \(\bigg[\)m.\(rac{m^2}{n}\).\(rac{m^3}{n^2}\)..........\(rac{m^3}{n^{n-1}}\)\(\bigg]\) = log \(\bigg[\)\(rac{m^{(1+2+3+4+......+n)}}{n^{(1+2+3+.....(n-1))}}\)\(\bigg]\)= log \(\bigg[\)\(rac{m^{rac{n(n+1)}{2}}}{n^{rac{n(n-1)}{2}}}\)\(\bigg]\) =  log \(\bigg[rac{m^{(1+n)}}{n^{(n-1)}}\bigg]^{rac{n}{2}}\)
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