For some integer q, every odd integer is of the forma)qb)q + 1c)2qd)2q...
Since q is an integer,
therefore...2q will absolutely be even,
and
2q+1=odd
For some integer q, every odd integer is of the forma)qb)q + 1c)2qd)2q...
We know that, odd integers are 1, 3, 5, ...
So, it can be written in the form of 2q + 1,
where, q = integer = Z
or q = ..., -1, 0,1,2,3, ...
∴ 2q + 1 = ..., -3, -1, 1, 3,5, ...
Alternate Method
Let 'a' be given positive integer. On dividing 'a' by 2, let q be the quotient and r be the remainder. Then, by Euclid's division algorithm, we have
a = 2q + r, where 0 ≤ r < />
⇒ a = 2q + r, where r = 0 or r = 1
⇒ a = 2q or 2q + 1
when a = 2q + 1 for some integer q, then clearly a is odd.
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.