...coefficient of the last term is 1, though it may be found by the rule Hence the 7th power of a -|- x is Examining the formation of the above coefficients,...dividing the product by the number which marks the place of that term. Thus the coefficient of the third term was found by multiplying 7, the coefficient of...

...of the last term is 1, though it may bs found by the rule 1X7 _ T~~ Henpe the 7th power of a -\- x is Examining the formation of the above coefficients,...dividing the product by the number which marks the place of that term. Thus the coefficient of the third term was found by multiplying 7, the coefficient of...

..._ j 7 Hence the 7th power of a + x is a7 -f- 7 a6 x + 21 aV + 35 aV+ 35 a3 z4 + 21 a'x' -\-Tax'+x7 Examining the formation of the above coefficients,...dividing the product by the number which marks the place of that term. Thus the coefficient of the third term was found by multiplying 7, the coefficient of...

...rule Hence the 7th power of a -f- x is a' +7a"ir +21 a6 a;* f- 35aV + 35 a' a4 +21 a* a;' + 7acc'+*' Examining the formation of the above coefficients,...observe, that each coefficient was found by multiplying th<3 co< fficient of the preceding term by the exponent of the leading quantity a in that term, and...

...first term is 1, that of the second is the name of the power, and in the following terms it is got by multiplying the coefficient of the preceding term by the exponent of the leading quantity in that term, and dividing the product by the number of that term. 5. That when the signs of both quantities...

...any term is formed from the coefficient of the preceding term. The coefficient of any term is formed by multiplying the coefficient of the preceding term by the exponent of x in that term, and dividing the product by the number of terms which precede the required term. For,...

...place is formed by means of the preceding coefficient. Ihe coefficient of a term of any place is formed by multiplying the coefficient of the preceding term by the exponent of x in this term, and dividing the product by the number of terms which precede that which is considered,...

...term is formed from the co-efficient of the preceding term. The co-efficient of any term is formed by multiplying the co-efficient of the preceding term by the exponent of x in that term, and dividing the product by the number of terms which precede the required term. P(m—n+l)...

...7_1 7' Hence the 7th power of a -f- x is a' -f-7aea: + 21 aV f-SSaV-p- 35a3a;4 + 21 a' x* + 1ax'+x' Examining the formation of the above coefficients,...coefficient of the preceding term by the exponent of the hurling quantity a in that term, and dividing the product by the number which marks the place of that...

...is the same as that of xr aC-'. See art [264]. Fourthly, that the coefficient of any term is formed by multiplying the coefficient of the preceding term by the exponent of x in that term, and dividing by the number of terms preceding the one in question. This rule is of...