Question

The number ${10}^n-1$ is divisible by $11$ for

• A. odd values of $n$
• B. even values of $n$
• C. all values of $n$
• D. not a multiple of $11$

Answer 1

Answer: (B)

even values of $n$

$Letabe{10}^n-1forn=1⟶{10}^1-1=9\to notdivisibleby11forn=2⟶{10}^2-1=99\to divisibleby11forn=3⟶{10}^3-1=999\to notdivisibleby11forn=4⟶{10}^4-1=9999\to divisibleby11forn=5⟶{10}^5-1=99999\to notdivisibleby11forn=6⟶{10}^6-1=999999\to divisibleby11So,byinductionwecansaythat{10}^n-1isdivisibleby11onlywhenniseven.$