Question

prove that 10²ⁿ⁻¹₊1 is divisible by 11 for all n∈N

Answer 1

Step-by-step explanation:

yes it's divisible

hope it helps you

Answer 2

Answer:

Step-by-step explanation

let n= 1

then p(1) = 10^(2+1) + 1

=10^3 + 1

=1001= 11(91)

it is true for n=1

let n=k and p(k) is true

then p(k) = 10 ^ (2k+1) +1 = 11m

let n=k+1

then p(k+1)= 10^ (2(k+1) + 1) + 1

= 10^ (2k+1+2) +1

=10^ (2k +1).10^(2)  +1

=(11m -1).10^(2) +1

=1100m-100+1=11(100m-9)

so p(k+1) is also true for n=k+1

therefore p(n) is true for all n∈N