Sum of GP members

Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?

Correct result:

s5 =  37.488
s =  37.5

Solution:

a1=30 a2=6 a3=1.2  r=a2/a1=6/30=15=0.2 r2=a3/a2=1.2/6=15=0.2 r=r2 a4=a3⋅ r=1.2⋅ 0.2=625=0.24 a5=a4⋅ r=0.24⋅ 0.2=6125=0.048  s5=a1+a2+a3+a4+a5=30+6+1.2+0.24+0.048=4686125=37.488
s=a1⋅ 11−r=30⋅ 11−0.2=752=37.5

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