For any natural number k , let $$a_{k}=3^{k}$$. The smallest natural number m for which $$\left\{(a_{1})^{1}

Question

For any natural number k , let $$a_{k}=3^{k}$$. The smallest natural number m for which $$\left\{(a_{1})^{1}	imes(a_{2})^{2}	imes...	imes(a_{20})^{20}ight\}<\left\{a_{21}	imes a_{22}	imes...	imes a_{20+m}ight\}$$, is

Accepted Answer

58. Given expression is \left\{(a_{1})^{1}	imes(a_{2})^{2}	imes...	imes(a_{20})^{20}ight\}&lt;\left\{a_{21}	imes a_{22}	imes...	imes a_{20+m}ight\} , { ( a 1 ) 1 × ( a 2 ) 2 × . . . × ( a 20 ) 20 } \left\{(a_{1})^{1}	imes(a_{2})^{2}	imes...	imes(a_{20})^{20}ight\} { ( a 1 ​ ) 1 × ( a

For any natural number k , let $a_{k}=3^{k}$ . The smallest natural number m for which $\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$ , is

For any natural number k , let $a_{k}=3^{k}$ . The smallest natural number m for which $\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$ , is

For any natural number k , let ak=3ka_{k}=3^{k}ak​=3k. The smallest natural number m for which \left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}&lt;\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}, is

For any natural number k , let ak=3ka_{k}=3^{k}ak​=3k. The smallest natural number m for which \left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}&lt;\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}, is

For any natural number k , let $a_{k}=3^{k}$ . The smallest natural number m for which $\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$ , is

For any natural number k , let $a_{k}=3^{k}$ . The smallest natural number m for which $\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$ , is