Use Mathematical Induction to Prove the Following for Every Positive $n$

question 94

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } \frac { 9 } { i ( i + 1 ) ( i + 2 ) } = \frac { 9 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }$

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Definitions:

DNA Molecule

The fundamental and distinctive structure of biological organisms, consisting of two long chains of nucleotides twisted into a double helix and responsible for genetic traits.

Epigenetic Mark

Chemical modifications to the DNA or surrounding proteins that affect gene expression without changing the DNA sequence and can be influenced by environmental factors.

Synapse

The junction between two neurons, facilitating the transmission of electrical or chemical signals from one neuron to the other.

Neurotransmitter

A chemical substance that transmits signals across a synapse between neurons in the nervous system.