![proof writing - Prove for all n∈N $1^2+3^2+5^2+...+(2n-1)^2=\frac{4n^3-n}{3}$ - Mathematics Stack Exchange proof writing - Prove for all n∈N $1^2+3^2+5^2+...+(2n-1)^2=\frac{4n^3-n}{3}$ - Mathematics Stack Exchange](https://i.stack.imgur.com/gkQWr.png)
proof writing - Prove for all n∈N $1^2+3^2+5^2+...+(2n-1)^2=\frac{4n^3-n}{3}$ - Mathematics Stack Exchange
By the principle of mathematical induction, prove that, for n ≥ 1 1^3 + 2^3 + 3^3 + ... + n^3 = (n(n + 1)/2)^2 - Sarthaks eConnect | Largest Online Education Community
![Induction Help: prove $2n+1< 2^n$ for all $n$ greater than or equal to $3$. - Mathematics Stack Exchange Induction Help: prove $2n+1< 2^n$ for all $n$ greater than or equal to $3$. - Mathematics Stack Exchange](https://i.stack.imgur.com/xxAPI.png)
Induction Help: prove $2n+1< 2^n$ for all $n$ greater than or equal to $3$. - Mathematics Stack Exchange
![How to #12 Proof by induction 1^3+2^3+3^3+...+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4 prove mathgotserved - YouTube How to #12 Proof by induction 1^3+2^3+3^3+...+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4 prove mathgotserved - YouTube](https://i.ytimg.com/vi/7tusni2xVS4/maxresdefault.jpg)
How to #12 Proof by induction 1^3+2^3+3^3+...+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4 prove mathgotserved - YouTube
![summation - Is there any. elementary formula for the sequence$\sum_{k=1}^{n }\left(2k-1\right)\left(\frac{1}{2}\right)^{k}$ - Mathematics Stack Exchange summation - Is there any. elementary formula for the sequence$\sum_{k=1}^{n }\left(2k-1\right)\left(\frac{1}{2}\right)^{k}$ - Mathematics Stack Exchange](https://i.stack.imgur.com/mMJNf.png)