2+5+10+17+...

1²+2²+3²+4²+...+n² = n(n+1)(2n+1)/6 = 1+4+9+16+...

Each term of your series is 1 more than the correspondimng
term in that series.

Since there are n terms, it's just the formula
for the sum of squares + n

Answer: 2+5+10+17+...(n²+1) = n(n+1)(2n+1)=/6 + n

You can do some algebra on that if you like, but that's the
answer.

Edwin