Give reason for the marked one

Give reason for the marked one Thus, the statement in (2) is established. Hence. by the prtnctpte induction, P(n) is true for all natural numbers. Example 6 Prove that 2.7 is divisible by 24, for all n e N. Solution Let the statement P(n) be defined as P(n) : 2.7" is diOsible by 24. Let Pot) 'note that POI) ame that P(k) We note that P(n) is true for n = l. since 2.7 3.5 — = 24. which is divi* pck) shall now prc Assume that P(k) is true nave 12 + 22 2.7k 3.5k -5 = N I.e. Now, we wish to prove that + l) is u-ue whenever P(k) is true. We have = 7 [24q 3.9 + + 15.9-5 = 7 24q -21.5' + 35 + -5 = 7 24q - + 30 'fore, + s true for a _iple 8 Prov ng pufncipl = 7 x 24q —6 (4Pi — 5) is a multiple of 4 (wb •on Let = 7 24q -24p = 24 (7q-p) P(nb : (ab Ne note th. k) be true, = 24 x r, r = 7q — p, is some natural number. (ab The expression on the R.H.S. of(l) is divisible by 24. Thus + 1) is now pr P(k) is true. Hence, by principle of mathematical induction, P(n) is true for all né