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Sum of infinite terms of G P 1/2-1/4+1/8-1/16-1/32.. is |
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Answer» Answer: Love Step-by-step explanation: As with any infinite series, the SUM {\displaystyle {\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots }\frac12+\frac14+\frac18+\frac{1}{16}+\cdots is DEFINED to mean the LIMIT of the partial sum of the first n terms {\displaystyle s_{n}={\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots +{\frac {1}{2^{n-1}}}+{\frac {1}{2^{n}}}}{\displaystyle s_{n}={\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots +{\frac {1}{2^{n-1}}}+{\frac {1}{2^{n}}}} as n approaches infinity. By various arguments,[a] one can show that this finite sum is equal to {\displaystyle s_{n}=1-{\frac {1}{2^{n}}}.}{\displaystyle s_{n}=1-{\frac {1}{2^{n}}}.} As n approaches infinity, the term {\displaystyle {\frac {1}{2^{n}}}}{\displaystyle {\frac {1}{2^{n}}}} approaches 0 and so SN tends to 1. |
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