Known: known 1 + 3 = 4 = 2,1 + 3 + 5 = 9 = 3,1 + 3 + 5 + 7 = 16 = 4, then 1 + 3 + 5 + + (2n + 1) = (n + 1) 1+3+5+… +(2n + 1) how to see that there are n + 1 items, list a process for me to see

Known: known 1 + 3 = 4 = 2,1 + 3 + 5 = 9 = 3,1 + 3 + 5 + 7 = 16 = 4, then 1 + 3 + 5 + + (2n + 1) = (n + 1) 1+3+5+… +(2n + 1) how to see that there are n + 1 items, list a process for me to see

From 1 + 3 can be seen as (3 + 1) / 2, 1 + 3 + 5 has (5 + 1) / 2, and so on 1 + 3 + 5 + 7 + +(2n + 1) has [(2n + 1) + 1] / 2 terms, which are n + 1 terms, and each equation is equal to the square of the number of terms, so 1 + 3 + 5 + +(2n+1)=(n+1)*(n+1)