Advertisements
Advertisements
Question
There are ______ natural numbers between n2 and (n + 1)2
Advertisements
Solution
There are 2n natural numbers between n2 and (n + 1)2
Explanation:
Natural number between n2 and (n + 1)2 will be calculated as follows:
= [(n + 1)2 – n2] – 1
= (n2 + 2n + 1 – n2) – 1
= 2n + 1 – 1
= 2n
Hence, there are 2n natural numbers between n2 and (n + 1)2.
APPEARS IN
RELATED QUESTIONS
Find the square of the given number.
71
Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of
1112 − 1092
Which of the following triplets are pythagorean?
(8, 15, 17)
Find the squares of the following numbers using diagonal method:
98
Find the square of the following number:
205
The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.
The sum of first n odd natural numbers is ______.
The sum of two perfect squares is a perfect square.
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
If x and y are integers such that x2 > y2, then x3 > y3.
