Mathematics inclined week #1: difficult category

problem:
prove, by mathematical induction, that:

you must show your working out either as a screenshot or by latex.
full solutions will be posted next week, along with a new question.

James is playing his favorite game at the arcade. after playing the game 3 times, he has 8 tokens remaining. he initially had 20 tokens, and the game costs the same number of tokens each time. the number tt of tokens james has is a function of gg, the number of games he plays

Given a circle with measures of (c, d, and r) and a circle with measures of (c', d', and r'), what is d if c c' = 12 and d' = 0.50? a) 3 b) 6 c) 12 d) 24

Suppose that in 2008 , 840,800 citizens died of a certain disease assuming the population of teh country is 399 miliion, what is the mortality rate in units of deaths per 100,000 people?