...r the common multiple or ratio, then may the series itself be represented by a, ar, ar', ar3, ar4, &c. which will evidently be an increasing or decreasing...unity than the number which denotes the place of that tei-m in the series. Hence, if the number of terms in the series be denoted by (я), the last term...

...r the common multiple or ratio, then may the series itself be represented by a, ar, ar", ar1, ar', &c. which will evidently be an increasing or decreasing...number or a proper fraction. In the foregoing series, theimlex ofrin any term is less by unity than the number which denotes the place of that term in the...

...the common multiplier or ratio ; then may the series itself be represented by a, ar, Mr3, ar3, ar*, &c., which will evidently be an increasing or decreasing...denotes the place of that term in the series. Hence, if the number of terms in the series be denoted by (n), the last term will be arn"1. 484. Let / be...

...the common multiplier or ratio ; then may the series itself be represented by a, ar, »ra, ar3, ar4, &c., which will evidently be an increasing or decreasing...proper fraction. In the foregoing series, the index of rm any term is less by unity than the number which denotes the place of that term in the series. Hence,...

...r the common multiple or ratio, then may the series itself be represented by a, ar, ar*, ar3, ar*, &c. which will evidently be an increasing or decreasing...the foregoing series, the index of r in any term is lass by unity than the number which denotes the place of that term in the series. Hence, if the number...

...the common multiplier or ratio ; then may the series itself be represented by a, ar, or1, ar3, rtr4, &c., which will evidently be an increasing or decreasing...r is a whole number, or a proper fraction. In the forgoing series, the index of r in any term is less by unity than the number which denotes the place...

...geometrical progression, then the second term will be Qr, the third ar2, the fourth ar3, &c., or, since the index of r in any term is less by unity than the number of terms, reckoning from the beginning, the last term will be ar"""1, when n denotes the number of...

...the common multiple or ratio, then may the series itself be represented by a, ar, ar", ar3, ar*, die. which will evidently be an increasing or decreasing...denotes the place of that term in the series. Hence, if the number of terms in the series be denoted by (n), the last term will be XXXII. On Arithmetical...

...series, and r the common multiplier or ratio ; then may the series itself be represented by a, ar, ar3, ar3, or4. &c., which will evidently be an increasing...denotes the place of that term in the series. Hence, if the number of terms in the series be denoted by (n), the last term will be arn~'. 429. Let I be...

...the common multiplier or ratio ; then may the series itself be represented by a, ar, ar2, ar2, arl, &c., which will evidently be an increasing or decreasing series, according as r is a whole number, or a pmper fraction. In the foregoiag series, the index of r in any term is less by unity than the number...