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PIMSO 2022 - Mathematics - Grade 9 / Secondary 3 - National Round Question 16

PIMSO Maths · PIMSO 2022 - Mathematics - Grade 9 / Secondary 3 - National Round

Question 16

If $S=\frac{10}{100}+\frac{200}{100^2}+\frac{3000}{100^3}+\frac{40000}{100^4}+\cdots+\frac{9000000000}{100^9}+\frac{100000000000}{100^{10}}$, what is $S+\frac1{10^9}$?