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Quadratic equation with a_{a} and a_{n+1} as a roots

Quadratic equation with a_{a} and a_{n+1} as a roots

jacks

Let

\mathbf{a_{n},a_{n+1}}

be the roots of the the equation

\mathbf{x^2+3nx+c_{n}=0}

for all

\mathbf{a_{1}=1}

. Then find value of

\mathbf{\displaystyle\sum_{n=1}^{2p}c_{n}=}

Reply 1

SimonM

We can find a recurrence for

a_n

using the fact that:

a_n+a_{n+1} = -3n

This then enables us to compute

c_n = a_n a_{n+1}

and so we can sum the series.

Quick Reply

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