iNVdtUTldN; §t! 



glVeri power, ami decreases continually oy i, in every 

 term to the last •, and in the following quantity the indices 

 of the terms are o» I, 2, 3, 4, Sec. 



2. To find the unkx or coefficients. The first is always 1, 

 iand the second Is the index of the power ; and in general, 

 if the coefficient of any term be multiplied by the index of 

 the leading quantity^ and the product be divided by the 

 number of terms to that place, it will give the coefficient 

 of the term next following. 



Note. The whole number of terms will bd onfe itiorcr 

 than the inc^ex of the given power ; and, when both terms 

 of the root are -f-, all the terms of the power will be -f- ; 

 but if the second term be -^, then all the odd terms will 

 be -f > and the even terms — . 



EXAMPLES. 



% . Lit a-\-K be involved to the fifth power. 



The terms without the coefficients will be 



and the coefficients will be 

 5X4 foX3 .^0X2 5X1 



or I, 5, 10, 10, 5, I ; 

 And therefore the 5th power is 

 a ^4"5^ V-}- 1 o^ ^A' ' -j- 1 o« ' :v ^ + 5(2.v ^-^-x ^. f 



2. Lei \ 



2 23 



b\ Sec. 



Note. The sum of the coefficieats, in every power, is equal 

 to the number 2, raided to that power. Thus, 14-1=2, for the 

 first power ; 1 -{-2 + 1=4=: 2^, for the square; i+3-f3-|-i=r 

 lzz2 ', for tho cube, or third power 5 and so qn. 



