Show that In + T15 -
n = 0, for n EN, n < 15
To show that
In + T15 - n = 0
for all n in the set of natural numbers such that n < 15, we can first express T15 in terms of n.
T15 = 1 + 2 + 3 + ... + 15
T15 = (15)(15 + 1) / 2
T15 = 15(16) / 2
T15 = 240
Now, we can substitute T15 into the original expression and simplify:
In + 240 - n
= n(n + 1) / 2 + 240 - n
= n^2/2 + n/2 + 240 - n
= n^2/2 - n/2 + 240
Now, we need to show that this simplifies to 0 for all n in the set of natural numbers such that n < 15:
n^2/2 - n/2 + 240 = 0
Let's try plugging in n = 1:
(1^2)/2 - 1/2 + 240 = 1/2 - 1/2 + 240 = 240 ≠ 0
Since the expression does not simplify to 0 for n = 1, we can conclude that the original statement is incorrect.