0 votes 0 votes Can't understand what they did here. How did they find out the value of xG(x)?Example 444. Chapter: Advanced Counting Techniques Mathematical Logic discrete-mathematics kenneth-rosen generating-functions + – MrPeppermint asked Dec 9, 2017 edited Mar 4, 2019 by Pooja Khatri MrPeppermint 561 views answer comment Share Follow See 1 comment See all 1 1 comment reply Ashwin Kulkarni commented Dec 9, 2017 reply Follow Share Let G(x) be a generating function means , we can write G(x) = a0x0 + a1x1 + a2x2 + ........ (basic principle of writing generating function ) Now xG(x) = a0x1 + a1x2 + a2x3 + ........ $\sum_{k=1}^{\infty }$ ak-1xk Now G(x) - 3xG(x) = [a0x0 + a1x1 + a2x2 + ........ ] - 3[a0x1 + a1x2 + a2x3 + ........] = a0x0 + (a1-3a0)x1 + (a2-3a1)x2 + ..... But given is ak-3ak-1 =0, Hence all the terms will be 0 except a0 = 2 3 votes 3 votes Please log in or register to add a comment.