Higher Algebra
Higher Algebra
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In our eReader you can find the full English version of the book. Read Higher Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Higher Algebra
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Hence the series is greater than i +1+1+1+1+ -, and is, therefore, divergent. 3d. When m < 1. In this case each term after the first is greater than the corre- sponding term of the series which, as shown above, is divergent. EXAMPLES CXXXIX Determine whether the following series are convergent or divergent : Scg. Compare with (2). 2. 1 + 3 + - + - + - + - + -+--. Solution. After the 5th term each term of this series is less than the corresponding term of the geometrical progression 4-4 4-4. 4 4. 4. 4. 4 whose ratio is |. Therefore, by I, the given series is convergent. 3. 1+1 + 1 + 1 + 1 + .... T 2 3 3 3 4 3 5 3 4^9^16 n 2 Sug. Compare with (3) . CONVERGENCT OF SERIES 357 584. Theorem. A series is convergent if, from the beginning or after a finite number of terms, the ratio of each term to the preceding term is less than some quantity which is itself less than 1. Dem. the series be S= \-k + l + m + n-\, a) =- + *H + ^ + -> (2) = ... + fcfi+i + ^+^ + .. \ k kl Mm .. ). (3) Now if the ratio of each term of (1) to the preceding term is less than p, we have from (3) S <...
What to read after Higher Algebra?
You can find similar books in the "Read Also" column, or choose other free books by John F John Florin Downey to read online
To quickly assess the difficulty of the text, read a short excerpt:
Hence the series is greater than i +1+1+1+1+ -, and is, therefore, divergent. 3d. When m < 1. In this case each term after the first is greater than the corre- sponding term of the series which, as shown above, is divergent. EXAMPLES CXXXIX Determine whether the following series are convergent or divergent : Scg. Compare with (2). 2. 1 + 3 + - + - + - + - + -+--. Solution. After the 5th term each term of this series is less than the corresponding term of the geometrical progression 4-4 4-4. 4 4. 4. 4. 4 whose ratio is |. Therefore, by I, the given series is convergent. 3. 1+1 + 1 + 1 + 1 + .... T 2 3 3 3 4 3 5 3 4^9^16 n 2 Sug. Compare with (3) . CONVERGENCT OF SERIES 357 584. Theorem. A series is convergent if, from the beginning or after a finite number of terms, the ratio of each term to the preceding term is less than some quantity which is itself less than 1. Dem. the series be S= \-k + l + m + n-\, a) =- + *H + ^ + -> (2) = ... + fcfi+i + ^+^ + .. \ k kl Mm .. ). (3) Now if the ratio of each term of (1) to the preceding term is less than p, we have from (3) S <...
What to read after Higher Algebra?
You can find similar books in the "Read Also" column, or choose other free books by John F John Florin Downey to read online
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