A sequence `x_1, x_2, x_3,....` is defined by letting `x_1=2` and `x_k=x_(k-1)/k` for all natural numbers `k,k>=2` Show that `x_n=2/(n!)` for all `n in N`.

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

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≥2 . Show that d_(n)=(2)/(n!) , for all n in N .

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≥2 . Show that d_(n)=(2)/(n!) , for all n in N .

A sequence x_0, x_1,x_2,x_3, ddot is defined by letting x_0=5 and x_k=4+x_(k-1) for all natural number kdot Show that x_n=5+4n for all ""n in N using mathematical induction..

A sequence a_1,a_2,a_3, ... is defined by letting a_1=3 a n d a_k=7a_(k-1) for natural numbers k ,kgeq2. Show that a_n=3.7_n-1 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 .

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

A set of n values x_(1), x_(2), ….., x_(n) has standard deviation sigma . The standard deviation of n values : x_(1) + k, x_(2) + k, ……, x_(n) + k will be :