Recent content by salubadsha

I thought of that too, it's called strong induction but I'm not too sure if what i did make sense. This is what i have Induction Hypothesis: Assume reuslt holds for n = 1, 2,... ,k for some intger k, k >= 1. Innduction Conclusion: Conisder n = k + 1 a|b_{k+1}x_{k+1} = a | b_{k-1}x_{k-1} +...

hey guys I'm stuck with another induction proof. Question: Suppose a, b1, b2,...,bn are integers with a|b1 (means a divides b), a|b2, ..., a|bn. Prove by induction on n that a|b1x1 + b2x2 + ... + bnxn for all integers x1, x2,..., xn. This is what i've, please let me know if it's...

nope sorry my bad, the correct statement is this: x + 2x^{2} + 3x^{3} + ... + nx^{n}= [ x - (n - 1)x^{n+1} + nx^{n+2} ] / (1-x)^{2} I did mutliply it and this is what i got: 1 + x + kx + kx^2 but then i don't know how to proof that (1+x)^k(1+x) ≥ 1 + (k + 1)x if i continue from here...

hey guys 1st week of my university and i got the painful assignment. I've not touched math from last 4-5 months, so I'm having trouble with few questions. Please help me out, thanks in advance 1- Prove that if x not equal 0, then x + 2x^{2} + 3x^{3} + ... + nx^{n}(1+x) = [ x - (n - 1)x^{n+1}...