Use the principle of mathematical induction :
A sequence `a_1, a_2, a_3,……` is defined by letting `a_1 = 3` and `a_k = 7a_(k-1)`, for all natural numbers k > 2 . Show that `a_n = 3.7^(n-1)` , for all natural numbers .

Use the principle of mathematical induction : A sequence d_1,d_2,d_3,……… is defined by letting d_1= 2 and d_k = (d_k - 1)/(k) , for all natural numbers, k gt= 2 . Show that d_n = (2)/(n!) , for all n in N

Use the principle of mathematical induction : A sequence b_0,b_1,b_2 ,….. Is defined by letting b_0 = 5 and b_k = 4+b_(k-1) , for all natural numbers k. show that b_n = 5 + 4n , for all natural number n using mathematical induction.

Use the principle of mathematical induction to show that (a^(n) - b^n) is divisble by a-b for all natural numbers n.

Prove the statement by the principle of mathematical induction : n^3 - 7n+ 3 is divisible by 3, for all natural number n .

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

Prove the statement by the principle of mathematical induction : 4^n - 1 is divisible by 3, for each natural number n .

Prove the following by using the principle of mathematical induction for all n in N (2n+1) lt 2^n , n >= 3

Prove the following by using the principle of mathematical induction for all n in N 3^n gt 2^n

Prove the statement by the principle of mathematical induction : 2^(3n) - 1 is divisible by 7, for all natural numbers n .