\(M=512-\frac{512}{2}-\frac{512}{2^2}-\frac{512}{2^3}-...-\frac{512}{2^{10}}\)

\(M=512-\frac{512}{2}-\frac{512}{4}-\frac{512}{8}-...-\frac{512}{1024}\)

\(M=\frac{1024}{2}-\frac{512}{2}-\frac{256}{2}-\frac{128}{2}-...-\frac{1}{2}\)

\(M=\frac{1024}{2}-\left(\frac{512}{2}+\frac{256}{2}+\frac{128}{2}+\frac{64}{2}+...+\frac{1}{2}\right)\)

\(M=\frac{1024}{2}-\frac{1023}{2}\)

\(M=\frac{1}{2}\)

\(M=0,5\)

Ta có :

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

\(1024^{10}=\left(1024^2\right)^5=\left(...76\right)^5=\left(...76\right)^{ }\)

Vậy chữ số tận cùng của số \(2^{100}\) là \(\left(...76\right)\)

Ta có : \(74^{814}=\left(74^2\right)^{407}=5476^{407}=\left(..............76\right)\)

\(51^{620}=\left(51^2\right)^{310}=2601^{310}=\left(......01\right)\)

Vì :

\(74^{814}+51^{620}=\left(.....76\right)+\left(.....01\right)=\left(......77\right)\)

Nên :

\(74^{814}+51^{620}\) có số tận cùng là \(\left(........77\right)\)