Find the sum of the first n terms of the series : `3 + 7 + 13 +21 + 31 +dot dot dot`

Answer

N/a

Explanation

Let `S_(n) = 3 + 7 + 13 + 21 + 31 + ... + T_(n)`
`(S_(n) = 3 + 7 + 13 + 21 + 31 + ... + T_(n -1) + T_(n))/(0 = [3 + 4 + 6 + 8 + 10 + ... + t_(n)] - T_(n))`
`T_(n) = 3 + {4 + 6 + 8 + 10 +...(n - 1)"terms"}`
`= 3 + (n - 1)/(2){2(4) + (n - 1 - 1)2}`
`= 3 + (n - 1)(n + 2) = n^(2) + n + 1`
`rArr` `S_(n) = sumn^(2) + sumn + sum1`
`= (1)/(6) n(n + 1)(2n + 1) + (1)/(2)n(n + 1) + n`
`= (1)/(6) n[(n + 1)(2n + 1) + 3(n + 1) + 6]`
`= (1)/(6) n(2n^(2) + 3n + 1 + 3n + 3 + 6)`
`= (1)/(6) n(2n^(2) + 6n + 10)`
`= (1)/(3) n(n^(2) + 3n + 5)`