Question

Tính nhanh:(\(1-\dfrac{1}{2^2}\)).(1-\(\dfrac{1}{3^2}\)).(1-\(\dfrac{1}{4^2}\))...(1-\(\dfrac{1}{10^2}\))

mik đag cần rất gấp giúp mik vs

Answer 1

Giải:

(1-1/2²).(1-1/3²).(1-1/4²).....(1-1/10²)

=3/2.2 . 8/3.3 . 15/4.4 . ... . 99/10.10

=1.3.2.4.3.5.....9.11/2.2.3.3.4.4.....10.10

=1.2.3.....9/2.3.4.....10 . 3.4.5....11/2.3.4.....10

=1/10.11/2

=11/20

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