How would you go about finding the first 25 digits after decimal point of $\displaystyle (\sqrt{10}+5)^{100}$? (without using calculator)
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To begin with $\displaystyle (1+x)^{1/2}=1+\frac{1}{2}x-\frac{1}{8}x^2+... $ $\displaystyle (1+9)^{1/2}=3(1+\frac{1}{9})^{1/2}=... $ You must evaluate number of terms needed for this accuracy. The same with $\displaystyle (1+x)^{100}=... $
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