简单英文数学问题(geometricsequence)findthesumtoinfinityofageometricsequencewhosesumtothreetermsis3968withasecondtermof640pleaseprocess,thanks

Question

简单英文数学问题(geometric sequence)
find the sum to infinity of a geometric sequence whose sum to three terms is 3968 with a second term of 640
please process,thanks

Answer 1

geometric sequence是等比数列呀
那么设公比是q
就有 640/q+640+640q=3968
所以640q^2-3328q+640=0
q=1/5 or q=5
q=5数列极限是正无穷 和当然也是正无穷吧
q=1/5 那么首项是3200 所以和极限就是3200/(1-q)=4000