A Treatise On Algebra

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Given the square root of 70, equal to 8. 36660 ; " " 74, " 8. 60233; 78, " 8. 83176; 82, " 9. 05539, to find the square root of 71.
Ans. 8. 42615.
(298. ) Fractions expanded into infinite series. When the dividend is not exactly divisible by the divisor, the quotient may be expressed by a fraction. Thus, if it is required to divide 1 by 1 a, we obtain the fraction .
We may, however, commence the division according to the usual method ; thus, I a - 3 +a 4 +, &c. , = the quotient.
a 4 Hence = l+a
...+ a +a 8 + 4 4-a 6 +, &c. , to infinity. Suppose a=^, we shall then have = T 2 which will be equal to the series Suppose a=J, we shall then have -= 1 = |, which will be equal to the series 1 Ex. 2. Resolve - - into an infinite series. 1+a Ans. L-a+a a a 8 + otc.
a a a a Ex. 4. Resolve ^ into an infinite series.


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