In an infinite GP series, each term is equal to th

Question

In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

Arun Kumar · Accepted Answer

Hello Student,3({r \over 1-r})=1 \=>3r=1-r \=>r={1 \over 4} \g_1+g_2=15 \=>g_1(1+r)=15 \=>g_1{ 5 \over 4}=15 \=>g_1=12 \=>\sum g={a \over 1-r}={12 \over {3\over 4}}=16 src=http://latex.codecogs.com/gif.latex?%5C%5Cg_1%2Cg_2%2Cg_3%2Cg_4%2Cg_5%2Cg_6.......g_%5Cinfty%20%5C%5Cg_1&plus;g_2%3D15%20%5C%5Cg_1%3D3%28%5Csum_%7B1%7D%5E%7B%5Cinfty%7Dg-g_1%29%3D3%28sum_%5Cinfty-g_1%29%20%5C%5C%3D3%28%7Bg_1%20%5Cover%201-r%7D-g_1%29%3D3%28%7Brg_1%20%5Cover%201-r%7D%29%20%5C%5C%3D%3E3%28%7Br%20%5Cover%201-r%7D%29%3D1%20%5C%5C%3D%3E3r%3D1-r%20%5C%5C%3D%3Er%3D%7B1%20%5Cover%204%7D%20%5C%5Cg_1&plus;g_2%3D15%20%5C%5C%3D%3Eg_1%281&plus;r%29%3D15%20%5C%5C%3D%3Eg_1%7B%205%20%5Cover%204%7D%3D15%20%5C%5C%3D%3Eg_1%3D12%20%5C%5C%3D%3E%5Csum%20g%3D%7Ba%20%5Cover%201-r%7D%3D%7B12%20%5Cover%20%7B3%5Cover%204%7D%7D%3D16>Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty

Magical Mathematics[Interesting Approach]> In an infinite GP series, each term is eq...

In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

muthhu swami , 10 Years ago

Arun Kumar

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Magical Mathematics[Interesting Approach]> In an infinite GP series, each term is eq...

In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

muthhu swami , 10 Years ago

Arun Kumar

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