Qwertyuiop[]
Junior Member
- Joined
- Jun 1, 2022
- Messages
- 123
[imath]\sum_{k=1}^{2n}\binom{2n}{k} 2^{-2k} 3^{2n-k}[/imath], i want to express this sum in binomial form but the problem is instead of (n choose k), i have (2n choose k) and the powers of coefficients are not n-k and k. Using the laws of indices i can factor out 2^-2 from 2^(-2k) to get [imath]2^{-2}\sum_{k=1}^{2n}\binom{2n}{k} 2^{k} 3^{2n-k}[/imath] But i can't rewrite 3^(2n-k) to 3^(n-k), I just need a hint.