Advertisements
Advertisements
प्रश्न
Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
Since, the number of terms in the given expression (a + b)n is 1 more than n
i.e., n + 1
APPEARS IN
संबंधित प्रश्न
Expand the expression: (2x – 3)6
Using Binomial Theorem, evaluate of the following:
(102)5
Using binomial theorem, evaluate f the following:
(101)4
Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Prove that `sum_(r-0)^n 3^r ""^nC_r = 4^n`
Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`
Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`
Find an approximation of (0.99)5 using the first three terms of its expansion.
Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
If n is a positive integer, find the coefficient of x–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`
Find the coefficient of x50 after simplifying and collecting the like terms in the expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ... + x1000 .
If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.
Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that O2 – E2 = (x2 – a2)n
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.
Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.
Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______.
