Question Number 93555 by mhmd last updated on 13/May/20
Commented by prakash jain last updated on 13/May/20
$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{i}}\end{pmatrix}\:{a}^{{i}} {b}^{{n}−{i}} =\left({a}+{b}\right)^{{n}} \\ $$$$\mathrm{Comparing}\:\mathrm{with}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{sum}=\left(\mathrm{1}+\mathrm{2}\right)^{\mathrm{100}} =\mathrm{3}^{\mathrm{100}} \\ $$
Commented by mhmd last updated on 13/May/20
$${thank}\:{you}\:{sir} \\ $$
Commented by mathmax by abdo last updated on 13/May/20
$$=\sum_{{k}=\mathrm{0}} ^{\mathrm{100}} \:\mathrm{2}^{{k}} \:{C}_{\mathrm{100}} ^{{k}} \:\:\:=\sum_{{k}=\mathrm{0}} ^{\mathrm{100}} \:{C}_{\mathrm{100}} ^{{k}} \:\mathrm{2}^{{k}} .\mathrm{1}^{\mathrm{100}−{k}} \:\:\:=\mathrm{3}^{\mathrm{100}} \:\Rightarrow{x}=\mathrm{3}\:{and}\:{y}=\mathrm{100} \\ $$