Advertisements
Advertisements
Question
Which of the following is larger? 9950 + 10050 or 10150
Advertisements
Solution
We have (101)50 = (100 + 1)50
= `100^50 + 50(100)^49 + (50*49)/(2*1) (100)^48 + (50*49*48)/(3*2*1) (100)^47 +` ......(1)
Similarly 9950 = (100 – 1)50
= `100^50 - 50 * 100^59 + (50*49)/(2*1) (100)^48 - (50*49*48)/(3*2*1) (100)^47 +` ....(2)
Subtracting (2) from (1), we get
10150 – 9950 = `2 50*(100)^49 + (50*49*48)/(3*2*1) 100^47 +` ....
⇒ 10150 – 9950 = `100^50 + 2 (50*49*48)/(3*2*1) 10^47 +` ....
⇒ 10150 – 9950 > 10050
Hence 10150 > 9950 + 10050
APPEARS IN
RELATED QUESTIONS
Expand the expression: (1– 2x)5
Expand the expression (1– 2x)5
Expand the expression: `(2/x - x/2)^5`
Expand the expression: (2x – 3)6
Using Binomial Theorem, evaluate the following:
(96)3
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`
Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`
Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.
If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
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 total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.
Find the coefficient of x15 in the expansion of (x – x2)10.
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 ______.
Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then ______.
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
The number of terms in the expansion of (x + y + z)n ______.
The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.
The positive integer just greater than (1 + 0.0001)10000 is ______.
