Given an example of a statement `P(n)` such that it is true of all `n Ndot`

Explanation

Consider the statement
`P(n):1^(2)+2^(2)+3^(2)+n^(2)=(n(+1)(2n+1))/(6)`
For n=1, `1=(1(1+1)(2xx1+1))/(6)`
`rArr1=(2(3))/(6)`
`rArr1=1`
For n=2, `1+2^(2)=(2(2+1)(4+1))/(6)`
`rArr5=(30)/(6)rArr5=5`
For n=3, `1+2^(2)+3^(2)=(3(3+1)(7))/(6)`
`rArr 1+4+9=(3xx4xx7)/(6)`
`rArr14=14`
Hence, the given statement is true for all n.