## mw647 one year ago Will fan and medal!!! Use mathematical induction to prove the property for all positive integers of n. [a^n]^2 = a^2n

1. mw647

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

2. butterflydreamer

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

3. butterflydreamer

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

4. mw647

Thank you so much!!

5. butterflydreamer

no probleem :)