\(0.99 = 1 - 0.01\)
\(∴(0.99)^5 = (1-0.01)^5\)
\(=\space^5C_0 (1)^5 - \space^5C_1 (1)^4 (0.01) +\space ^5C_2 (1)^3 (0.01)^2 \) (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 \(0.951.\)
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is:
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
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