Russian Maths Olympiad Question l Which is Larger❓‎@apnaexamhour

[@jameshogge]

Alternative solution:
1.005^200 = (1 + 0.005)^200
If you expand that out you get
1^200 + 200 * 1^199 * 0.005 + ...
Call all the later terms S and you have
1 + 200*0.005 + S
= 1 + 1 + S
= 2 + S
S we know to be non-zero and positive therefore 2 + S > 2

[@apnaexamvlog]

👍

[@선플라워-s3u]

1² we define the real.

[@ccarniver]

Can't I use this proof to prove that 2 < 1.005 ^ 100?