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3 years ago

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What is the sum of the sequence 1+3+5+7+...+99 Use Gauss's approach to find the following sum.

1 answer:

jenyasd209 [6]3 years ago

5 0

Gauss's approach is to add the same sequence in reverse order, namely

S=1+3+5+7+......+95+97+99
S=99+97+95+......+7+5+3+1
---------------------------------------
2S=(1+99)+(3+97)+(5+95)+......(95+5)+(97+3)+(99+1)=50*100=5000
=> sum = (2S)/2 = 5000/2=2500.

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Answer:

$\boxed{\bold{-21x^3y^4}}$

Explanation:

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[ $\boxed{\bold{Final \ Answer}}$ ]

➤ $\bold{-21x^3y^4}$

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Read 2 more answers

Write a quadratic equation given the roots -1/3 and 5, show your work

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$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

<u>Answer</u>

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

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