-
Call Us
+91 8076753736 -
Send us an Email
[email protected]
Sets
Show by mathematical induction that a2n – b2n is divisible by a + b.
Let is divisible by a + b
I. For n = 1,
is divisible by a + b is divisible by a + b
(a - b) (a + b) is divisible by a + b
which is true.
∴ P(1) is true.
II. Suppose the statement is true for n = m,
is divisible by a + b
...(i)
III. For n = m + 1
P (m + 1): is divisible by a + b.
Now,
From (i),
where k' =
is divisible by a + b
∴ P(m + 1) is true
∴ P(m) is true P ( m + 1) is true
Hence, by the principle of mathematical induction, P(n) is true for all
Sponsor Area
Sponsor Area