Share Tool + Management Kdan Cloud Topic 5 Questions Outlines A= Q Search Sequences and Series A 171% FAX Tv Tv □ v OV T OCR Q Comment & Markup Annotation Editor OCR Convert Fax Search 115. When throwing a dice, the probability to obtain six at the first throw is 1. When throwing a dice twice, the probability to obtain the first six at the second throw (that is, to obtain no six at the first throw and six at the second throw) is ½½. The probability to obtain the first six at the third throw (that is, to obtain no six at the first two throws and six at the third throw) is ... The probability to obtain the first six at the fourth throw is. In this way the probability can be determined to obtain the first six at the fifth throw, at the sixth throw etc. We denote the probability to obtain the first six at the nth throw as pn. (a) Find a formula for the general term pn. 6 (b) Does the series p₁ + p2+p3+p4+... have a finite result? Calculate the result if it is finite. (c) Tania and Julia take turns to throw the dice. Tania starts. The first one to obtain six gets an icecream. The probability that Tania is the first one to obtain six is given by p₁+p3+p5+p7+... (this is the probability to obtain the first six at the first throw or at the third throw or at the fifth throw or at the seventh throw or...). Find the result of this sum. (d) The probability to throw at most n times before obtaining the first six is given by t₁ +t2+3+ t4+...+t. Find this probability. 116. A rubber ball falls from a height of 8.1 meter. Each time the ball touches the ground, it bounces back up to 2/3 of the height from which it last fell. Find the total distance covered by the ball. (Consider the ball as a point.) 117. Tony, Mary, Andy and Jane each have a savings account that yields a 4% interest rate per year. Interest is paid out every December 31st for the money that was in the account December 31st the previous year. (a) On December 31st, 2017, Tony deposits €1000 into his account. To what amount will this deposit have grown by January 1st, 2023? (b) From 2017 on, Mary will deposit €1000 into her account on every last day of the year, for ten years (so her last deposit is on December 31st, 2026). What amount will be in her account on January 1st, 2028? (c) Andy will deposit €1000 into his account on every last day of the year, starting in 2017. He will continue until some January 1st, he has (more than) €25 000 in his account. In which year will this be? 5 17