In mathematics, we use a form of complete induction called  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

The principle of mathematical induction is one such tool which can be used to prove a wide variety of  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

P(n) is true for all  1122425276inductive hypothesismathematical inductionmathematical statementsnatural numbers n.

The assumption that the given statement is true for n = k in the inductive step is called the  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

 1122425276inductive hypothesismathematical inductionmathematical statementsnatural is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number.

P(n):2.7ⁿ+3.5ⁿ−5, ∀n∈N is divisible by  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

For every natural number n, n(n²−1)is divisible by  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

10²ⁿ⁻¹ + 1 is divisible by  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

If n∈N,then 7²ⁿ+2³ⁿ⁻³.3ⁿ⁻¹ is always divisible by  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

When 2³⁰¹ is divided by 5, the least positive remainder is  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.

For all n∈N,41ⁿ−14ⁿ is a multiple of  1122425276inductive hypothesismathematical inductionmathematical statementsnatural.