Question

simplify and express in index (1-(1-(1-n)^-1)^-1

Answer 1

Hope u like my process.
======================
${(1 - {(1 - {(1 - n)}^{ - 1} )}^{ - 1}) }^{ - 1} \\ = {(1 - (1 - \frac{1}{1 - n} ) ^{ - 1} )}^{ - 1} \\ = {(1 - {( \frac{1 - n - 1}{1 - n}) }^{ - 1} )}^{ - 1} \\ = {(1 - {( \frac{ - n}{1 - n} )}^{ - 1} )}^{ - 1} \\ = {(1 - {( \frac{n}{n - 1} )}^{ - 1} )}^{ - 1} \\ = {(1 - \frac{n - 1}{n} )}^{ - 1} \\ = {(1 - 1 + \frac{1}{n}) }^{ - 1} \\ = {( \frac{1}{n} )}^{ - 1} = n$
Hope this is ur required answer
Proud to help you