Hello fellow IT Support friends!
I've some maths problems i cant solve and hopes someone can help me.
1) For each of the following relations on the set {1, 2, 3, 4}, decide whether it is reflexive,
symmetric, anti-symmetric and/or transitive.
i) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}
ii) {(1, 3), (1, 4), (2, 3), (3, 4)}
iii) {(1, 1), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 3), (3, 4)}
2) What is the coefficient of x^2 y^7 in (x + y)^9 ?
3) Prove that 12+32+52+…+ (2n+1)2 = (n+1) (2n+1) (2n+3)/3 whenever n is a nonnegative integer.
Thanks again!
Originally posted by 93'guy:Hello fellow IT Support friends!
I've some maths problems i cant solve and hopes someone can help me.
1) For each of the following relations on the set {1, 2, 3, 4}, decide whether it is reflexive,
symmetric, anti-symmetric and/or transitive.i) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}
ii) {(1, 3), (1, 4), (2, 3), (3, 4)}
iii) {(1, 1), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 3), (3, 4)}2) What is the coefficient of x^2 y^7 in (x + y)^9 ?
3) Prove that 12+32+52+…+ (2n+1)2 = (n+1) (2n+1) (2n+3)/3 whenever n is a nonnegative integer.
Thanks again!
You would have better chances at the Homework Forum. I'll give questions 2 and 3 a try anyway:
2. 9 x 8 / 2 = 36 - http://en.wikipedia.org/wiki/Binomial_coefficient
3.
12 + 32 + 52...
= 20(1 + 2 + 3 +...+ n) - 8n
= 20(n * [n+1] / 2) - 8n
= 4{5n * [n+1] / 2 - 2n}
= 4{(5n2 + 5n) / 2 - 2n}
= 4(5n2 + n) / 2}
= 2(5n2 + n)
...did I miss anything?