Question

Will fan and medal!!!

Use mathematical induction to prove the property for all positive integers of n.
[a^n]^2 = a^2n

Answer 1

\[\left[ a^n \right]^2 = a^2n\]

Answer 2

step 1: Prove true for n = 1 (since we want to prove for all positive integers.
So, sub n=1 into LHS and RHS.
\[LHS = \left[ (a^n)^2 \right] = \left[ (a^1)^2 \right] = a^2 \]
\[RHS = \left[ a^2n \right] = a^2 (1) = a^2 \]
\[\therefore LHS = RHS \]
\[\therefore true .for . n = 1 \]

Answer 3

step 2: Assume true for n = k

(for this step, you just sub n=k into your equation "(a^2)^n = a^2n")

Required to true for n = k + 1

(here, sub n = k+1 into the equation)

Step 3: write the proof thinggy

Answer 4

Thank you so much!!

Answer 5

no probleem :)