Sum it up Jeff Bivin -- LZHS

1 + 3 + 9 + 27 + 81 + 243 a1 = 1 r = 3 n = 6 Jeff Bivin -- LZHS

4 - 8 + 16 - 32 + 64 – 128 + 256 a1 = 4 r = -2 n = 7 Jeff Bivin -- LZHS

Alternative Sum Formula We know that: Multiply by r: Simplify: Substitute: Jeff Bivin -- LZHS

Find the sum of the geometric Series Jeff Bivin -- LZHS

Find the sum of all the terms in the following GP. 10, 30, 90, ….7290 r = 3, n = ? an = 7290 Jeff Bivin -- LZHS

Find the sum of all the terms in the following GP. 4, 8, 16, ….2048 r = 2, n = ? an = 2048 Jeff Bivin -- LZHS

Evaluate = 2 + 4 + 8+…+1024 a1 = 2 r = 2 n = 10 an = 1024 Jeff Bivin -- LZHS

Evaluate = 3 + 6 + 12 +…+ 384 a1 = 3 r = 2 n = 8 an = 384 Jeff Bivin -- LZHS

an = a1·r(n-1) Review -- Geometric Sum of n terms nth term Jeff Bivin -- LZHS

Geometric Infinite Series Jeff Bivin -- LZHS

The Magic Flea (magnified for easier viewing) There is no flea like a Magic Flea Jeff Bivin -- LZHS

The Magic Flea (magnified for easier viewing) Jeff Bivin -- LZHS

Sum it up -- Infinity Jeff Bivin -- LZHS

Remember --The Magic Flea Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

rebounds ½ of the distance from which it fell -- A Bouncing Ball rebounds ½ of the distance from which it fell -- What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 128 feet tall building? 128 ft 64 ft 32 ft 16 ft 8 ft Jeff Bivin -- LZHS

A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft Downward = 128 + 64 + 32 + 16 + 8 + … 128 ft 64 ft 32 ft 16 ft 8 ft Jeff Bivin -- LZHS

A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft Upward = 64 + 32 + 16 + 8 + … 128 ft 64 ft 32 ft 16 ft 8 ft Jeff Bivin -- LZHS

A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft Downward = 128 + 64 + 32 + 16 + 8 + … = 256 Upward = 64 + 32 + 16 + 8 + … = 128 TOTAL = 384 ft. 128 ft 64 ft 32 ft 16 ft 8 ft Jeff Bivin -- LZHS

rebounds 3/5 of the distance from which it fell -- A Bouncing Ball rebounds 3/5 of the distance from which it fell -- What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 625 feet tall building? 625 ft 375 ft 225 ft 135 ft 81 ft Jeff Bivin -- LZHS

A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft Downward = 625 + 375 + 225 + 135 + 81 + … 625 ft 375 ft 225 ft 135 ft 81 ft Jeff Bivin -- LZHS

A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft Upward = 375 + 225 + 135 + 81 + … 625 ft 375 ft 225 ft 135 ft 81 ft Jeff Bivin -- LZHS

A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft Downward = 625 + 375 + 225 + 135 + 81 + … = 1562.5 Upward = 375 + 225 + 135 + 81 + … = 937.5 TOTAL = 2500 ft. 625 ft 375 ft 225 ft 135 ft 81 ft Jeff Bivin -- LZHS

Find the sum of the series Jeff Bivin -- LZHS

Fractions - Decimals Jeff Bivin -- LZHS

Let’s try again + + Jeff Bivin -- LZHS

One more subtract Jeff Bivin -- LZHS

OK now a series Jeff Bivin -- LZHS

.9 = 1 .9 = 1 That’s All Folks Jeff Bivin -- LZHS