# Find value of A

#### Albert

##### Well-known member
find value of A:

$A=\dfrac {1+2^{200}+4^{200}+5^{200}+10^{200}+10^{200}+20^{200}+25^{200}+50^{200}+100^{200}} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

#### anemone

##### MHB POTW Director
Staff member
Hey Albert, I can solve this one!

$A=\dfrac {1+2^{200}+4^{200}+5^{200}+10^{200}+10^{200}+20^{200}+25^{200}+50^{200}+100^{200}} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

$A=\dfrac {1+\left(\frac{100}{50}\right)^{200}+\left(\frac{100}{25}\right)^{200}+\left(\frac{100}{20}\right)^{200}+\left(\frac{100}{10}\right)^{200}+\left(\frac{100}{10}\right)^{200}+\left(\frac{100}{5}\right)^{200}+\left(\frac{100}{4}\right)^{200}+\left(\frac{100}{2}\right)^{200}+100^{200}} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

$A=\dfrac {1+100^{200}\left((\frac{1}{50})^{200}+(\frac{1}{25})^{200}+(\frac{1}{20})^{200}+(\frac{1}{10})^{200}+(\frac{1}{10})^{200}+(\frac{1}{5})^{200}+(\frac{1}{4})^{200}+(\frac{1}{2})^{200}+1\right)} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

$A=\dfrac {100^{200}\left((\frac{1}{100})^{200}+(\frac{1}{50})^{200}+(\frac{1}{25})^{200}+(\frac{1}{20})^{200}+(\frac{1}{10})^{200}+(\frac{1}{10})^{200}+(\frac{1}{5})^{200}+(\frac{1}{4})^{200}+(\frac{1}{2})^{200}+1\right)} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

$A=\dfrac {100^{200}\left(1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}\right)} {1+2^{-200}+4^{-200}+5^{-200}+10^{-200}+10^{-200}+20^{-200}+25^{-200}+50^{-200}+100^{-200}}$

$A=100^{200}$

#### Albert

##### Well-known member
anemone :
perfect ! you got the answer