Verified answer

1 = 1²

1 + 3 = 2²

Assume for n=m

1 + 3 + 5 + ... + (2m-1) = m²

Add (2m+1) to both sides

1 + 3 + 5 + ... + (2m-1) + (2m+1) = m² + 2m + 1

1 + 3 + 5 + .... (2m+1) = (m+1)²

If it is true for n=m then it must be true for n=m+1

It is true for n=1

Hence it must be true for n=2

By induction it must be true for all values of n if n≥1

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