`7^(2n)+2^(3n-3)*3^(n-1)` is divisible by 25

1.	`7^(2n)+2^(3n-3)*3^(n-1)` is divisible by 25
Answer» by appliying the mathematical induction formula, we have, `(7^2)^n + (2^3)^(n-1) * 3^(n-1)` `(49)^n + (8)^(n-1).3^(n-1)` `49^n + 24^(n-1)` `(50-1)^n + (25-1)^(n-1)` `.^nC_0(50)^n - .^nC_1(50)^(n-1) .....................- .^(n-1)C_(n-1)(-1)^(n-1) ` `25k + (-1)^n + (-1)^(n-1)` now, if n= odd then n-1 = evenand if n= even then n-1 = oddtherefore the term ` underbrace((-1)^n + (-1)^(n-1) )` is always going to be zero (0)therefore, the equation will be as = 25kso, it is divisible by 25.

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