# Telescoping : Product it or sum it

Algebra Level 1

$1 - \frac{1}{{\color{#3D99F6}2}} + \frac{1}{{\color{#3D99F6}2}} - \frac{1}{{\color{#D61F06}3}} +\frac{1}{{\color{#D61F06}3}} - \frac{1}{{\color{#20A900}4}} + \frac{1}{{\color{#20A900}4}} - \cdots = 1$ This infinite telescoping sum converges to $1,$ partly because all the terms except $1$ get cancelled.

Can we say that the infinite telescoping product below also converges to $1$ for a similar reason?

$\frac{1}{{\color{#3D99F6}2}} \times \frac{{\color{#3D99F6}2}}{{\color{#D61F06}3}} \times \frac{{\color{#D61F06}3}}{{\color{#20A900}4}} \times \frac{{\color{#20A900}4}}{{\color{#624F41}5}}\times \frac{{\color{#624F41}5}}{{\color{#E81990}6}} \times \frac{{\color{#E81990}6}}{7} \times {\cdots } = 1$

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