Question

Ex 5. (15 points total] For a natural integer n > 2, define n := V1+V1+ V1 +.. n times For instance ra = V1 + V1+V1+vī. (5a) (5 points) Write ræ+1 in function of In. (5b) (10 points) Prove that for all natural integers n > 2, In & Q.

prove by induction!

Answer 1

59 8n z N IHNIINH...NT - ntl times That+NI+NANTIAN n times So enton ra squarning both sides then 81 2 1 = ton 8 = rnt 1 Ans. 56 8n & Q & natural integess h22 Step I n=2, then 8a = Alta = Niti T 82=12 as na is irrational 0 Step II let n=k, So assume that statement in equation is true for n=k so sx & 9 Now, for n=kti KHI = NINHALANT SR+=NITOR SKA = 178k Shell = 8k If Skt EQ then S 2 EQ f then SKAT I EQ R EQ (by equation 2 which is contradiction (by equation ) 80 rkt, & 0 Statement is true for n=kt/ statement one is free for all natural number n32.