Question:
Find an approximation of (0.99)5 using the first three terms of its expansion
Find an approximation of (0.99)5 using the first three terms of its expansion
Updated On: Jan 23, 2026
Hide Solution
Verified By Collegedunia
Solution and Explanation
\(0.99 = 1 - 0.01\)
\(∴(0.99)^5 = (1-0.01)^5\)
\(=\space^5C_0 (1)^5 - \space^5C_1 (1)^4 (0.01) +\space ^5C_2 (1)^3 (0.01)^2 \) (Approximately)
\(=1-5(0.01)+10(0.01)^2\)
\(=1-0.05+0.001\)
\(=1.001-0.05\)
\(= 0.951\)
Thus, the value of \((0.99)^5 \) is approximately \(0.951.\)
Was this answer helpful?
0
0
Top Questions on Binomial theorem
- If
\[ A = \begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix}, \]
then the determinant of the matrix \( A^{2025} - 3A^{2024} + A^{2023} \) is
- JEE Main - 2026
- Mathematics
- Binomial theorem
- If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to
- JEE Main - 2026
- Mathematics
- Binomial theorem
\[ \left( \frac{1}{{}^{15}C_0} + \frac{1}{{}^{15}C_1} \right) \left( \frac{1}{{}^{15}C_1} + \frac{1}{{}^{15}C_2} \right) \cdots \left( \frac{1}{{}^{15}C_{12}} + \frac{1}{{}^{15}C_{13}} \right) = \frac{\alpha^{13}}{{}^{14}C_0 \, {}^{14}C_1 \cdots {}^{14}C_{12}} \]
Then \[ 30\alpha = \underline{\hspace{1cm}} \]
- JEE Main - 2026
- Mathematics
- Binomial theorem
- The coefficient of \(x^{48}\) in \[ (1+x) + 2(1+x)^2 + 3(1+x)^3 + \cdots + 100(1+x)^{100} \] is equal to
- JEE Main - 2026
- Mathematics
- Binomial theorem
- The sum of the coefficients of \(x^{499}\) and \(x^{500}\) in \[ (1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\cdots+x^{1000} \] is:
- JEE Main - 2026
- Mathematics
- Binomial theorem
View More Questions
Questions Asked in CBSE Class XI exam
- Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5
- Write the resonance structures for SO3 , NO2 and NO3-
- CBSE Class XI
- Kossel-Lewis Approach to Chemical Bonding
- How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
- CBSE Class XI
- permutations and combinations
- The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10–19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: FeSO4, MnCl2, ZnCl2 and CdCl2. in which of these solutions precipitation will take place?
- CBSE Class XI
- Law Of Chemical Equilibrium And Equilibrium Constant
- The story is divided into pre-War and post-War times. What hardships do you think the girl underwent during these times?
- CBSE Class XI
- The address
View More Questions
Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.