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MATH / Compute

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Compute ∑n=1∞1FnFn+2,\sum_{n = 1}^\infty \frac{1}{F_n F_{n + 2}},where FnF_n denotes the nnth Fibonacci number, so F0=0F_0 = 0 and F1=1.F_1 = 1.
Plain-text mathematical notation (without MathML)
Compute
∑_(n=1)^(∞)(1)/(F_(n)F_(n+2)),where F_(n) denotes the nth Fibonacci number, so F₀=0 and F₁=1.
Original LaTeX notation
Compute
\[\sum_{n = 1}^\infty \frac{1}{F_n F_{n + 2}},\]where $F_n$ denotes the $n$th Fibonacci number, so $F_0 = 0$ and $F_1 = 1.$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
0ae6e025-86d1-5aae-81a6-770e81831ff2
task_key
intermediate~5falgebra--test--0ae6e025-86d1-5aae-81a6-770e81831ff2
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import