State why the series the summation from n equals 1 to infinity of the quotient of 5 and 2 raised to the n minus 1 power is convergent or divergent, and if it is convergent, find the sum.

Question

State why the series  is convergent or divergent, and if it is convergent, find the sum. 

Answer 1

The series is geometric with r<1 or convergent. The trick is to identify the A/R in the series.

Recalling exponential laws:

5/2^*n-1) = 5/2^n * 5/2^-1 = 10/2^n or expanded 10(1 + .5 +.5^2 +.5^3..etc) So A = 10, R = 1/2 and then Sum = a/(1-r) or 20.