How do I prove by mathmatical induction that 211221231241

How do I prove by mathmatical induction that:
(2(1)-1)+(2(2)-1)+(2(3)-1+(2(4)-1) +.............. + (2(n)-1) = n^2

Prove by mathematical induction: (2(1) - 1) + (2(2) - 1) + (2(3) - 1) + (2(4) - 1) + + (2(n) - 1) = n^2

Solution

We have (2*1-1) = 2-1= 1 = 1², (2*1-1) + (2*2-1)= (2-1)+ (4-1) = 1+3 = 4 = 2², (2*1-1) + (2*2-1)+(2*3-1) = 4+(6-1) = 4+5 = 9 = 3²

Hence, by induction, we have (2*1-1) + (2*2-1)+(2*3-1) +…+ ( 2*n-1) = n²