# FMM11

### From charlesreid1

# Friday Morning Math Problem

## Inferring Rule from Sequence

1 = 1 1 - 4 = -(1 + 2) 1 - 4 + 9 = 1 + 2 + 3 1 - 4 + 9 - 16 = -(1 + 2 + 3 + 4)

Guess the general law suggested by these examples, express it in suitable mathematical notation, and prove it.

Solution |
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The general law is:
This can be proved for the base case of n=1, in which case above equation reduces to 1=1 Then can show that if assume n is true, then n+1 holds If you split the left side into the sum from k=1 to n, (which can be reduced to a single term by using the identity above for the case of n, which you assume is true), and the last n+1 term written explicitly, you can do some algebraic manipulation to show it's equivalent to the right side. |

## Flags

Friday Morning Math ProblemsSpider Socks and Shoes FMM1 Sums of Powers of 2 FMM2 Fifty Coins FMM3 The Zeta Monogram FMM4 The Cthulhus Monogram FMM4B Multiplication Logic FMM5 The Termite and the Cube FMM6 Sharing Dump Trucks FMM7 The Flippant Juror FMM8 Bus Routes FMM9 A Robust Bus System FMM9B Square-Free Sequence FMM10 Inferring Rule from Sequence FMM11 Checkerboard Color Schemes FMM12 One-Handed Chords FMM13 First Ace FMM14 Which Color Cab FMM15 Petersburg Paradox Revisited FMM16 A Binomial Challenge FMM17 A Radical Sum FMM18 Memorable Phone Numbers FMM19 Arrange in Order FMM20 A Pair of Dice Games: FMM21
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