Question

Find the approximate sum of the series shown below.

Answer 1

Answer:

$The~expression=7(\frac{5}{3})^{(1-1)}+ 7(\frac{5}{3})^{(2-1)}+7(\frac{5}{3})^{(3-1)}+7(\frac{5}{3})^{(4-1)}+7(\frac{5}{3})^{(5-1)}\\~~~~~~~~~~~~~~~~~~~~~~=7(\frac{5}{3})^0+7(\frac{5}{3})^1+7(\frac{5}{3})^2+7(\frac{5}{3})^3+7(\frac{5}{3})^4\\~~~~~~~~~~~~~~~~~~~~~~=7(1)+\frac{35}{3}+7(\frac{25}{9})+7(\frac{125}{27}) +7(\frac{625}{81})\\~~~~~~~~~~~~~~~~~~~~~~=7+\frac{35}{3}+\frac{175}{9}+\frac{875}{27} +\frac{4375}{81}$

$=\frac{7(81)}{81}+\frac{35(27)}{3(27)} +\frac{175(9)}{9(9)} +\frac{875(3)}{27(3)}+\frac{4375}{81}\\=\frac{7(81)+35(27)+175(9)+875(3)+4375}{81}\\=\frac{10087}{81}\\=124.53086~(approximate)$