#8 MATHEMATICAL INDUCTION Prove that 3[5^(2n + 1)] + 2^(3n + 1) is divisible by 17

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By Using Mathematical Induction Prove that (49)^n + 16n - 1 is divisible by 64

Prove that 3[5^(2n + 1)] + 2^(3n + 1) is divisible by 17

Prove that 2[4^(2n + 1)] + 3^(3n + 1) is divisible by 11

Prove that 1 + 2 + 3 + ...... + n = n(n+1) by 2

Prove that 1^2 + 2^2 + 3^2 + ...... + n^2 = n(n+1)(2n+1) by 6

Prove that 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ....... = n (n + 1)^2 (n + 2) by 12

Prove that 1 / 1.3 + 1 / 3.5 + 1 / 5.7 + ...... = n by 2n + 1

Prove that 1 / 1.4 + 1 / 4.7 + 1 / 7.10 + ...... = n by 3n + 1

Prove that 1.2.3 + 2.3.4 + 3.4.5 + ...... = n(n+1)(n+2)(n+3) by 4

Prove that 2 + 3.2 + 4.2^2 + ...... = n.2^n

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