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 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 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.

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

Let P(n) be statement and let P(k) rArr P(k+1) ,for some natural number k, then P(n) is true for all n in N

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

Prove each of the statements by the principle of mathematical induction : sqrtn lt (1)/(sqrt1) + (1)/(sqrt2) + (1)/(sqrt3) + …….+ (1)/(sqrtn) , for all natural numbers n gt= 2

Prove the following by using the principle of mathematical induction for all n in N 1+2+3+…….+n lt 1/8 (2n+1)^2

By using the principle of mathematical induction , prove the follwing : P(n) + 1+3+5+……….+(2n-1) = n^2 , n in N

Prove the following by the principle of mathematical induction: \ 11^(n+2)+12^(2n+1) is divisible 133 for all n in Ndot