Track / Stage 4 / 126 of 340 #386 of 1964

Aerith thinks $(1.4)^{(1.4)^{(1.4)}}$ is well-defined, but Bob thinks it diverges. Who is right?

Your answer

Check

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Show the answer

Next problem →

Official solution

Because $(1.4)^{2}=1.96<2$, the tetrations of 1.4 can never surpass 2, so the expression does not diverge to infinity; Aerith is right.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.