Let there be a sequence of integers a_1, a_2, a_3, ... For all a_i written as a base 10 number, multiply it by 5^100 and write it in base 10, replace each digit with its remainder when divided by 2, and read that number as if it's binary. Call that number a_(i+1). Prove that if a_1 is any positive integer less than 2^101, the sequence is periodic and has period 2^k for some k.

y do u put "subscirbe to ence" on a app for ppl who need with their work?

step-by-step explanation:

its 512 because parenthesis and to the 2nd power is 512 so it will be 512

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.