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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

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  1. mw647
    • one year ago
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    \[\left[ a^n \right]^2 = a^2n\]

  2. butterflydreamer
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Thank you so much!!

  5. butterflydreamer
    • one year ago
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    no probleem :)

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