`7.5^(2n-1) + 2^(3n+1)` is divisible by 17 for every natural` n ge 1`.

5^n -1 is divisible by 4.

3^(2(n-1)) + 7 is divisible by 8 for every natural n ge 2 .

5^(2(n-4) -6n + 32 is divisible by 9 for every natural number n ge 5 .

4^(n+1) + 15n + 14 is divisible by 9 for every natural number n ge 0 .

7^(2n) + 2^(3n-3) 3^(n-1) is divisible by 25 for any natural number n gt 1 .

1/(n+1) + 1/(n+2)+…..+ 1/(3n+1) gt 1 for every positive integer n.

Show that the function f: N rarr N, given by f(1) f(2)= 1 and f(x) = x - 1 for every x gt 2, is onto but not one-one.

2^n gt n , n is a natural number.

If a_1, a_2,........,a_n are in G.P. and a_i gt 0 for every i, then find the value of [[loga_n, loga_(n+1),loga_(n+2)],[loga_(n+1),loga_(n+2),loga_(n+3)],[loga_(n+2),loga_(n+3),loga_(n+4)]]

Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan^(-1) |("1n ((5)/(2)))/(1 + 1n 2 1n 5)| . Note Angle between two curves is the angle between their tangents at the point of intersection.