Find the sum of the geometric sequence. three divided by two, three divided by eight, three divided by thirty two, three divided by one hundred and twenty eight, three divided by five hundred and twelve

Answer: we have that[3/2,3/8,3/32,3/128,3/512]the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]=(1/512)*[256*3+64*3+16*3+4*3]=(3/512)*[256+64+16+4]=(3/512)*[340]=(1020/512)=255/128---------> 1.9922the answer is1.9922another way to calculate it is through the following formula∑=ao*[(1-r^n)/(1-r)]where ao---------> is the first termr----------> is the common ratio between termsn----------> is the number of termsao=1.5r=1/4-----> 0.25n=5so∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99Step-by-step explanation: we have that[3/2,3/8,3/32,3/128,3/512]the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]=(1/512)*[256*3+64*3+16*3+4*3]=(3/512)*[256+64+16+4]=(3/512)*[340]=(1020/512)=255/128---------> 1.9922the answer is1.9922another way to calculate it is through the following formula∑=ao*[(1-r^n)/(1-r)]where ao---------> is the first termr----------> is the common ratio between termsn----------> is the number of termsao=1.5r=1/4-----> 0.25n=5so∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99