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### Question

Determine the pattern in the successive sums from the previous question. what will be the sum of fib(1)+fib(2)+fib(3)+fib(4)+fib(5)+fib(6)+fib(7)+fib(8)+fib(9)+fib(10)?

### Answer #1 for Questions: Determine the pattern in the successive sums from the previous question. what will be the sum of fib(1)+fib(2)+fib(3)+fib(4)+fib(5)+fib(6)+fib(7)+fib(8)+fib(9)+fib(10)?

**Answer:**

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1 Patterns in the Fibonacci Numbers

1.1 The Final Digits

1.2 Digit Sums

1.2.1 A new research question for you to try

1.3calculator Fibonacci Number Digit Sums Calculator

2 Factors of Fibonacci Numbers

2.1/ You do the maths…

2.2 A nice factorisation of F(2n)

3 Every number is a factor of some Fibonacci number

3.1 Are there any numbers n where FEP(n) = n?

3.2 FEP(n) = n – 1

3.3 FEP(n) = n + 1

3.4 FEP(n) = n + 5

3.5 Other patterns in FEP(n)

3.6calculator Fibonacci Factors Calculator

3.7 Fibonacci Numbers with Index number factor

3.8 Fibonacci numbers where i ± 1 is a factor of Fib(i)

3.8.1/ You do the maths…

3.9 The first Fibonacci number with a given prime as a factor: FEP(p) for prime p

4 Fibonacci common factors

4.1 Neighbouring Fibonacci Numbers have no common factors

5 Fibonacci Numbers and Primes

5.1 Fibonacci numbers and special prime factors

5.2 Fib(prime) and Carmichael’s Theorem

5.3 No primes next to Fibonacci’s!

5.4 Almost no primes next to Fibonacci’s powers either!!

5.5 A Prime Curio

5.6 Another Prime Curio

5.7 More Links and References on Prime Numbers

6 Remainders after division or Fibonacci MOD n

6.1 calculator Fibonacci Number Remainder (mod) cycles Calculator

6.2 Some interesting facts about Pisano periods

6.3 A fast algorithm for computing Pisano periods?

6.4 Pisano Periods for moduli 2 – 299

6.5 The relationship between the Pisano Period mod n and FEP(n)

6.5.1/ You do the maths…

7 Benford’s Law and initial digits

7.1/ You do the maths…

7.2 When does Benford’s Law apply?

7.2.1/ You do the maths…

8 Every number starts some Fibonacci Number

8.1 Is there a Fibonacci number that ends with any given number?

9 The Fibonacci Numbers in Pascal’s Triangle

9.1 Why do the Diagonals sum to Fibonacci numbers?

9.2 Another arrangement of Pascal’s Triangle

9.3 Fibonacci’s Rabbit Generations and Pascal’s Triangle

9.4 calculator A Galton’s Quincunx Simulator

9.4.1/ You do the maths…

10 The Fibonacci Series as a Decimal Fraction

10.1 A Generating Function for the Fibonacci Numbers

10.2 Fibonacci decimals

10.3 calculator An exact Fractions Calculator

10.3.1/ You do the maths…

11 A Fibonacci Number Trick

11.1 A Lightning Calculation

11.2 So how did Alice do it?

11.3 Why does it work?

11.4 calculator Practice here with “Bill”

12 Another Number Pattern

13 Fibonacci Numbers and Pythagorean Triangles

13.1 Using the Fibonacci Numbers to make Pythagorean Triangles

13.2 calculator Pythagorean Triples from Fibonacci-type Series Calculator

13.3 Fibonacci Numbers as the sides of Pythagorean Triangles

13.3.1 Square Fibonacci Numbers

13.4 Other right-angled triangles and the Fibonacci Numbers

13.4.1/ You do the maths…

14 Maths from the Fibonacci Spiral diagram

15 ..and now it’s your turn!

15.1/ You do the maths…

### Answer #2 for Questions: Determine the pattern in the successive sums from the previous question. what will be the sum of fib(1)+fib(2)+fib(3)+fib(4)+fib(5)+fib(6)+fib(7)+fib(8)+fib(9)+fib(10)?

**Answer:**

[tex](8.13 times { { {yx83 > frac{x97 geqslant frac{yxxy times – { { {521. = 0}^{2} }^{2} }^{2} times frac{?}{?} }{?} }{?} }^{2} }^{2} }^{2} [/tex]

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