An Important Theorem - Practice Questions & MCQ

Finding nature of an integral part of the expression.

If the given expansion is in the form of 

Working rule:

Step 1: 

Step 2: Use N + N’ or N - N’ such that result is an integer

I.e. 

Step 3: Now use the concept greatest integer function and fractional part of a function, N = I + f, where I is an integral part of N i.e., [N] and f is a fractional part of N, i.e. { N }.

For example, the integral part of  is an even number.

Now consider, 

Use,

Hence, integral part of   is an even integer