Question

Use induction to show that $a^{n} \geq 1+na$ for all $a\geq 2$ and for all n sufficiently large

Answer 1

Ans fixat ufau we a 2 y chaose sh Now we tast the proot, let n-3 (utt larye) / 2 t 2X2 ey 7 4 241+2x 4 0 16 9 Hence, we conclude tha t TS 2 1+2n Now, we pYove thI vesult tor nt 2H 222 (1+2n) 2t4n 2 +2n t2n 02 2n4 > 2n+2(n+1リ> 1+2( nt1) n3 ntl 2 1+2 (ntl) pooveやt Htnte 2" 1+2n for n 3

Now wil ntart chooke a= 3 we we the Prove n= 2 2 3 1+ 3X2 g7 n= 3 1+ 3x3 33408 2.7 10 Co naequemthy, we Aay that 90 001 3 1t 3n Nouw we pYove the reAt 3H 33" 3 (1+3n) 3 + 9n 3+ 3n t 6n 3 (nt1 )+ 6n 1+3 (nt1) o m2 UH 32 1+3n Hence pyove that can show that, So, we

a 1tna Autt arge 4 n