Induction Gayness (1 Viewer)

[Dreamerish*~]

Prove by induction that:

3¹ + 3² + 3³ + ... + 3ⁿ < 3^{n + 1}

Thanks.

 

[acmilan]

True for n = 1

Assume true for n = k

3¹ + 3² + 3³ + ... + 3^k < 3^k+1

For n = k+1

3¹ + 3² + 3³ + ... + 3^k + 3^{k + 1}
< 3^k+1 + 3^k+1
= 2.3^k+1
< 3.3^k+1
= 3^k+1+1
= 3^k+2

Hence 3¹ + 3² + 3³ + ... + 3^k + 3^k+1 < 3^k+2

and so forth...

 

[Dreamerish*~]

Gosh, that was fast.

Thank you.