M2(Mathematical Induction~)

務必詳細列式~

Proved by mathematical induction that the statements are true for all positive integers.

1). [2^(2n-1)]+[3^(2n-1)] is divisible by 5.

2). (n^3)+5n is divisible by 6.



3a). Prove by Mathematical Induction that,
1*3+2*(3^2)+3*(3^3)+...+n*(3^n)=(3/4)[(2n-1)*(3^n)+1]

3b). Hence show that 1+2*3+3*(3^3)+...+100*(3^99)=(1/4)[199*(3^100)+1]