1. and everything started because someone wanted to count when we should be closest part of me is still so alone wait a part of me is always detached its not something you can turn off is that.. counting the touches of her fingertips thats the fibonacci sequence touch touch touch touch 7ouch touch touch touch touch toudh 7ouch touoh whatever i did to deserve you it couldn't hae been enough abstracting, looking at numbers and patterns.) the fibonacci numbers will be denoted by {f,} where fi = 1, f2 = 1, and f, = fn-1 + fn-2 for all n> 2. (a) (10 points) write in some orderly manner the values of fi through f20. (b) (15 points) which fibonacci numbers are even? (look at the subscripts.) why does this pattern appear? (c) (10 points) there are sequences of numbers related to the fibonacci numbers. one is the se quence of lucas numbers. these are defined by v = 1, u2 = 3, and vn = v-1+0n-2 for all n > 2. write in some orderly manner the values of vi through vio. if we were going to define vo, what should its value be? (d) (15 points) we will find the sum of the first n fibonacci numbers with odd subscripts. find the first 5 such sums and guess what such a sum is equal to in general .formula for the sum of the first n fibonacci numbers with even subscripts (e) (15 points) guess a s (f) (15 points) guess a formula for the sum of the first n fibonacci numbers (g) (20 points) prove the result found in (d).