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PIMSO 2022 - Mathematics - Senior Secondary - National Round Question 18

PIMSO Maths · PIMSO 2022 - Mathematics - Senior Secondary - National Round

Question 18

Find $\sqrt{S+\frac1{10^9}}$ if $$S=\frac{10}{100}+\frac{200}{100^2}+\frac{3000}{100^3}+\frac{40000}{100^4}+\cdots+\frac{9000000000}{100^9}+\frac{100000000000}{100^{10}}.$$

Input format: use pi, sqrt(...), ^ for powers, * for multiplication and / for division as needed.