-
Looking for HSC notes and resources? Check out our Notes & Resources page
another question :S (1 Viewer)
- Thread starter vanush
- Start date
darkliight
I ponder, weak and weary
Summing the RHS of all those equations we have:
1 + x + 2x + x2 + 2x2 + 2x2 + x3 + 2x3 + 2x3 + 2x3 ...
= 1 + x + x2 + x3 + 2x + 2x2 + 2x2 + 2x3 + 2x3 + 2x3 ...
= 1 + x + x2 + x3 + 2x + 4x2 + 6x3 ...
= sum_{n=0}^{\infty} xn + 2nxn
= sum_{n=0}^{\infty} (1+2n)xn
1 + x + 2x + x2 + 2x2 + 2x2 + x3 + 2x3 + 2x3 + 2x3 ...
= 1 + x + x2 + x3 + 2x + 2x2 + 2x2 + 2x3 + 2x3 + 2x3 ...
= 1 + x + x2 + x3 + 2x + 4x2 + 6x3 ...
= sum_{n=0}^{\infty} xn + 2nxn
= sum_{n=0}^{\infty} (1+2n)xn