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How do you find the sum of the geometric series #Sigma 5* 2^(n-1)# n=1 to 9?

1 Answer

Shwetank Mauria

Nov 18, 2016

Sum of first #9# terms is #2560#

Explanation:

In this geometric series first term #a_1=5.2^(1-1)=5*1=5# and common ratio #r# is #2#, as second term is #a_2=5.2^(2-1)=5*2=10# and #a_2/a_1=10/5=2#

The sum of such a series for first #n# terms is given by

#S_n=a_1xx(r^n-1)/(r-1)# and hence #S_n=5xx(2^n-1)/(2-1)#, as #a_1=5# and #r=2# and

Sum of first #9# terms is #5xx(2^9-1)/(2-1)=5xx512/1=2560#

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