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hey all, need a bit of help with this question thanks in advance.

hey all, got a q, doesn't seem too hard but i cant get LHS=RHS in last step RTP: 1^2 + 2^2 + ... + (n-1)^2 + n^2 + (n-1)^2 + ... + 2^2 + 1^2 =\frac{n(2n^2+1)}{3}

Hi all, Can someone help spot my error? Answer is n=17 apparently. Q: A card is selected from a pack, its suit is noted, and it is returned. How many times must this be done so that the probability of at least one heart is more than 99%? P(X>=1) = 1-P(X=0) > 0.99 P(X=0) < 0.01 solve for n...

Hi All, Answer says C, but D also works right? \sqrt{i^3}=\sqrt{-1}=\pm{\frac{1}{\sqrt{2}}(1-i)=\pm{\frac{1}{\sqrt{2}}(-1+i) \quad \theta=\frac{3\pi}{4}, \frac{-\pi}{4}

Hi all, Whats another way we can do this without having to find all the roots of i, or just a less time consuming method? Thanks in advance.

Hi all, Just want to check if i can use this formula to solve questions like this. Works every time and saved me a lot of working.

Hi all, This has been a tricky question that ive been stuck on for a while, not sure if its even possible. If you manage to get it please share the solutions.

Hi all, Need help with 'strong' induction, a few questions on this topic in cambridge but they don't provide examples so im not sure how it differs from normal induction (n=1, n=k, n=k+1). Any help is appreciated. Example below:

From cambridge ext 1 yr 12 8D 11) Suppose that OABC is a parallelogram. Let M be the midpoint of OA and let P be the point of intersection of MC and OB. Prove using vectors, that: OP = (1/3)*OB

Hi Mathematicians, I need help on question D, i think it's impossible to solve. Question asks: a 5 digit number is chosen at random. Find the probability: d) that the digits are distinct and in increasing order. Good luck!