- #1
Dish
- 2
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Hey guys, I'm just totally stumped by this Q
Use mathematical induction to prove that for integer n, n > or = to 2,
(x+1)^n - nx - 1 is divisible by x^2.
It's not a Homework problem.
Attempt at solution:
1) Prove for n =2,
(x+1)^2 - 2x - 1 = x^2 + 2x +1 - 2x -1 = x^2
2) Assume true for n = k
thus (x+1)^k -kx -1 = m x^2 where m is any integer
3) Prove for n = k+1
(x+1)^(k+1) - (k+1)x - 1
(x+1)^k . (x+1) - kx - x - 1
(x+1)^k - kx -1 + x(x+1)^k - x - 1
m.x^2 + x(x+1)^k - x -1
from here on i am totally confused. :S
Please can someone help me to finish the proof, so that it's divisible by x^2?
Thank you :)
Use mathematical induction to prove that for integer n, n > or = to 2,
(x+1)^n - nx - 1 is divisible by x^2.
It's not a Homework problem.
Attempt at solution:
1) Prove for n =2,
(x+1)^2 - 2x - 1 = x^2 + 2x +1 - 2x -1 = x^2
2) Assume true for n = k
thus (x+1)^k -kx -1 = m x^2 where m is any integer
3) Prove for n = k+1
(x+1)^(k+1) - (k+1)x - 1
(x+1)^k . (x+1) - kx - x - 1
(x+1)^k - kx -1 + x(x+1)^k - x - 1
m.x^2 + x(x+1)^k - x -1
from here on i am totally confused. :S
Please can someone help me to finish the proof, so that it's divisible by x^2?
Thank you :)