solve this stpe by step

this is how to solve: 0:01

• WE WANT TO FIND THE INFINITE SUM OF A GEOMETRIC SEQUENCE, 0:04 IF IT EXISTS. 0:05 SO BECAUSE WE'RE DETERMINING A SEQUENCE, 0:07 WE CAN ALSO CALL THIS A GEOMETRIC SERIES. 0:10 THE INFINITE SUM WILL EXIST 0:12 IF THE ABSOLUTE VALUE OF R IS LESS THAN 1. 0:16 REMEMBER, R IS THE COMMON RATIO 0:18 BETWEEN SUCCESSIVE TERMS GIVEN HERE. 0:21 IT'S ALSO THE CONSTANT WE WOULD MULTIPLY BY 0:24 TO FIND EACH SUCCESSIVE TERM. 0:28 IF WE'RE NOT ABLE TO LOOK AT THE TERMS IN THE SERIES 0:31 TO DETERMINE THE VALUE OF R, 0:33 AGAIN, WE CAN USE THIS FORMULA HERE 0:35 WHERE R = "A" SUB N DIVIDED BY "A" SUB N - 1 0:39 WHICH MEANS TO FIND R, WE CAN SELECT ANY TERM IN THE SEQUENCE 0:43 AND DIVIDE BY THE TERM BEFORE IT. 0:45 IN THIS CASE, IT'LL BE EASIEST TO SELECT THE FIRST TWO TERMS. 0:49 SO R = 2 DIVIDED BY 5 OR 2/5. 0:56 NOTICE HOW THIS DOES MEET THE REQUIREMENT 0:58 WHERE THE ABSOLUTE VALUE OF R IS LESS THAN 1, 1:00 AND THEREFORE WE CAN FIND THIS INFINITE SUM 1:03 USING THIS FORMULA HERE. 1:04 OUR INFINITE SUM, S, IS GOING TO BE EQUAL TO THE FIRST THE TERM, 1:08 "A" SUB 1 WHICH IS 5 DIVIDED BY 1 - R OR 1 - 2/5. 1:19 WELL 1 IS THE SAME AS 5/5. 1:21 5/5 - 2/5 = 3/5, SO NOW WE HAVE 5 DIVIDED BY 3/5. 1:29 LET'S WRITE THIS AS MULTIPLICATION. 1:31 SO INSTEAD OF 5, WE'LL 5/1 AND THEN INSTEAD OF DIVIDING BY 3/5, 1:36 WE'LL MULTIPLY BY THE RECIPROCAL WHICH SHOULD BE 5/3 1:41 WHICH MEANS THEIR INFINITE SUM = 25/3. 1:53 SO EVEN THOUGH THIS SUM IS INFINITE, IT = 25/3 1:57 BUT NOTICE HOW EACH TERM IN THE SERIES 2:00 IS GETTING SMALLER AND SMALLER APPROACHING 0 2:02 WHICH IS THE REASON WHY WE'RE ABLE TO FIND THIS INFINITE SUM 2:06 OF THE GEOMETRIC SEQUENCE. 2:07 LET'S TAKE A LOOK AT A SECOND EXAMPLE. 2:11 AGAIN, WE'RE TOLD THIS IS A GEOMETRIC SERIES, 2:14 SO THE FIRST STEP IS TO FIND THE VALUE OF R 2:16 TO SEE IF IT MEETS THE CONDITION 2:18 WHERE THE ABSOLUTE VALUE OF R IS LESS THAN 1. 2:22 AGAIN, LET'S GO AHEAD AND USE THE FIRST TWO TERMS. 2:26 SO R IS GOING TO BE EQUAL TO "A" SUB 2 DIVIDED BY "A" SUB 1 2:31 OR 3 DIVIDED BY -8 OR -3/8. 2:36 WELL THE ABSOLUTE VALUE OF -3/8 IS 3/8 WHICH IS LESS THAN 1, 2:41 SO ONCE AGAIN WE CAN FIND THIS INFINITE SUM. 2:45 THE INFINITE SUM IS EQUAL TO THE FIRST TERM "A" SUB 1 2:48 WHICH IS -8 DIVIDED BY 1 - R, SO WE'LL HAVE 1 - -3/8 2:58 WHICH WILL BECOME -8 DIVIDED BY 1 + 3/8. 3:05 WELL 1 IS THE SAME AS 8/8, 8/8 + 3/8 = 11/8, 3:10 SO YOU HAVE -8 DIVIDED BY 11/8 3:15 WHICH IS THE SAME AS -8/1 x THE RECIPROCAL OF 11/8 OR 8/11. 3:23 SO THE INFINITE SUM = -64/11. 3:28 NOTICE HOW THIS INFINITE SUM IS NEGATIVE. 3:31 AND HOPEFULLY THAT MAKES SENSE, BECAUSE NOTICE -8 OUR FIRST TERM 3:35 IS THE SMALLEST NUMBER IN THE SERIES, 3:37 +3 WOULD BE THE LARGEST VALUE IN THE SERIES, 3:40 AND THEREFORE THE NEGATIVES WILL OUTWEIGH THE POSITIVES 3:43 GIVING US A -INFINITE SUM. 3:46 OKAY. I HOPE YOU FOUND THESE TWO EXAMPLES HELPFUL.