Which among the following is the least number that will divide `7^(2n)-4^(2n)` for every positive integer n? [4,7,11,13]

Which one of the following is true? a) (1+(1)/(n))^(n)ltn^(2),n is a positive integer b) (1+(1)/(n))^(n)lt2,n is a positive integer c) (1+(1)/(n))^(n)ltn^(3),n is a positive integer d) (1+(1)/(n))^(n)ge2,n is a positive integer

How many terms are there in the expansion of (1+x)^2n (n is a positive integer)?

Which of the following species has the shortest bond length? N_2^(+) , N_2 , N_2^(-) , N_2^(2-)

if ^(2n+1)p_(n-1):^(2n-1)p_n=3:5 , prove that n = 4

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

Consider the following statement : P(n):A^n=[[1+2n,-4n],[n,1-2n]] for all ninN Write P(1) .

(a)For every positive integer n, 7^n-3^n should be divisible by (2,3,4,8).

If A{ x: x is a natural number,x 7} , then n(A) is