With the help of the principle of mathematical induction, how do you prove that 1*2+3*4+5*6+…+ (2n-1) *2n=n(n+1) (4n- 1) /3? - Quora
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