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SASMO 2022 Grade 8 Question 25

SASMO · SASMO 2022 Grade 8

Question 25

It is given that $$\frac1A=\frac2{1+2^2+2^4}+\frac3{1+3^2+3^4}+\frac4{1+4^2+4^4}+\cdots+\frac{10}{1+10^2+10^4}.$$ For any positive real number $x$, $[x]$ is the greatest integer less than or equal to $x$; for example, $[2.35]=2$. Find $[A]$.

Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).