Question

what is the product of geometrical proggresion​

Answer 1

Consider a GP : a, ar, ar², ar³, ar⁴,..., arⁿ⁻¹ with n tems.

So, the product of All the terms of GP is :

$a .ar.a {r}^{2} .a {r}^{3} .....a {r}^{n - 1}$

$(a.a.a....(n - times)).(r ^{1 + 2 + 3 + ... + n - 1} )$

${a}^{n} . {r}^{ \frac{(n)(n - 1)}{2} }$

${(a.r ^{ \frac{n - 1}{2} } )}^{n}$