<Dl> <Dd> k (k + 1) 2 + (k + 1). (\ displaystyle (\ frac (k (k + 1)) (2)) + (k + 1) \, .) </Dd> </Dl> <Dd> k (k + 1) 2 + (k + 1). (\ displaystyle (\ frac (k (k + 1)) (2)) + (k + 1) \, .) </Dd> <Dl> <Dd> k (k + 1) 2 + (k + 1) = k (k + 1) + 2 (k + 1) 2 = (k + 1) (k + 2) 2 = (k + 1) ((k + 1) + 1) 2 (\ displaystyle (\ begin (aligned) (\ frac (k (k + 1)) (2)) + (k + 1) & = (\ frac (k (k + 1) + 2 (k + 1)) (2)) \ \ & = (\ frac ((k + 1) (k + 2)) (2)) \ \ & = (\ frac ((k + 1) ((k + 1) + 1)) (2)) \ end (aligned))) </Dd> </Dl> <Dd> k (k + 1) 2 + (k + 1) = k (k + 1) + 2 (k + 1) 2 = (k + 1) (k + 2) 2 = (k + 1) ((k + 1) + 1) 2 (\ displaystyle (\ begin (aligned) (\ frac (k (k + 1)) (2)) + (k + 1) & = (\ frac (k (k + 1) + 2 (k + 1)) (2)) \ \ & = (\ frac ((k + 1) (k + 2)) (2)) \ \ & = (\ frac ((k + 1) ((k + 1) + 1)) (2)) \ end (aligned))) </Dd>

What is principle of mathematical induction explain with the help of an example