...to 0 ; while the exponents of b increase by unity from 0 up to the required power of the binomial. The sum of the exponents of a and b in any term is equal to the exponent of the power required. Thus, in the second power, the sum of the exponents of a and b in each...

...to 0 ; while the exponents of b increase by unity from 0 up to the Required power of the binomial. The sum of the exponents of a and b in any term is equal to the exponent of the power required. Thus, in the second power, the sum of the exponents of a and b in each...

...obvious that this will always be the case, to whatever extent the involution may be carried. Also, the sum of the exponents of a and b in any term is equal to the exponent of the power required. Thus, in the second power, the sum of the exponents of a and b in each...

...until we reach the last term in which the exponent is the same as that of the required power. (131.) The sum of the exponents of a and b in any term is equal to the exponent of the given power. Thus, in the second power, the sum of the exponenta of a and b in each...

...which the exponent of h exceeds 12; and, in general, it follows from the mode in which Q is found that the sum of the exponents of a and b in any term cannot exceed their sum in the first term ; in other words, the sum of the two highest exponents cannot...

...term, the second power in the third term, and the exponent of b is one greater in each succeeding term. The sum of the exponents of a and b in any term is n. III. The coefficient of the first term is 1 ; of the second term, n ; of the third term, — * -...

...the first three coefficients are repeated in inverse order after the third term. Hence we note that The sum of the exponents of a and b in any term of the expansion is equal to the exponent of the binomial. The number of terms in the expansion is...

...that term and divided by the number of the term, equals the coefficient of the next term. NOTE 1. — The sum of the exponents of a and b in any term is the same as the exponent of the power. NOTE 2. — The coefficients and exponents of the last half...

...fifth term in the expansion of is 10х2-ь4 = Г>. (vi.) The signs of the terms are all positive when the terms of the binomial are both positive ; the...the binomial exponent. (viii.) The coefficients of two terms equally distant from the beginning and the end of the expansion are equal. In a subsequent...

...in the expansion of (tt + b)" is 10x2 --4 = 5. (vi.) Tlie siyns of the terms are all positive wJien the terms of the binomial are both positive ; the...negative. Observe, as a check : (vii.) The sum of the exj)onents of a and b in any term is equal to the binomial exponent. (viii.) The coefficients of two...