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9. Establish the identity $1 + z + z^2 + ... + z^n = \frac{1 - z^{n+1}}{1 - z}$ $(z \neq 1)$

          9. Establish the identity
$1 + z + z^2 + ... + z^n = \frac{1 - z^{n+1}}{1 - z}$ $(z \neq 1)$
        
9. Establish the identity
1 + z + z^2 + ... + z^n = (1 - z^n+1)/(1 - z) (z ≠ 1)

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Establish the identity 1+z+z^(2)+cdots+z^(n)=(1-z^(n+1))/(1-z),(z)!=(1) 9. Establish the identity 1- zn+1 1+z+z2+...+z= 1-z (z 1)
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00:01 An equation we have to verify whether this equation is an identity or not we start by considering right -hand side that is 2 minus cos z divided by 1 plus cos z we multiply and divide this both by 1 minus cos z we get this now in numerator we get 2 minus 2x z minus cos z plus cos square z and in denominator we use…
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