Advertisements
Advertisements
Question
Using binomial theorem, indicate which is larger (1.1)10000 or 1000.
Solution
We have:
(1.1)10000
\[= (1 + 0 . 1 )^{10000} \]
\[ =^{10000}{}{C}_0 \times \left( 0 . 1 \right)^0 + ^{10000}{}{C}_1 \times (0 . 1 )^1 +^{10000}{}{C}_2 \times (0 . 1 )^2 + . . . ^{10000}{}{C}_{10000} \times (0 . 1 )^{10000} \]
\[ = 1 + 10000 \times 0 . 1 + \text{ other positive terms } \]
\[ = 1 + 10000 + \text{ other positive terms } \]
\[ = 10001 + \text{ other positive terms } \]
\[ \because 10001 > 1000\]
\[ \therefore (1 . 1 )^{10000} > 1000\]
APPEARS IN
RELATED QUESTIONS
Find the ratio of the coefficients of xp and xq in the expansion of \[\left( 1 + x \right)^{p + q}\] .
Write last two digits of the number 3400.
If a and b are the coefficients of xn in the expansion of \[\left( 1 + x \right)^{2n} \text{ and } \left( 1 + x \right)^{2n - 1}\] respectively, find \[\frac{a}{b}\]
If \[\left( 1 - x + x^2 \right)^n = a_0 + a_1 x + a_2 x^2 + . . . + a_{2n} x^{2n}\] , find the value of \[a_0 + a_2 + a_4 + . . . + a_{2n}\] .
If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then ris equal to
The coefficient of \[x^{- 17}\] in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] is
The coefficient of xn in the expansion of (1 + x)2n and (1 + x)2n–1 are in the ratio ______.
If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then value of n is ______.
If A and B are coefficient of x n in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then `A/B` equals ______.
The largest coefficient in the expansion of (1 + x)30 is ______.
The ratio of the coefficients of xp and xq in the expansion of (1 + x)p + q is ______.
If 2515 is divided by 13, the reminder is ______.
The sum of the series `sum_(r = 0)^10 ""^20C_r` is `2^19 + (""^20C_10)/2`
The expression 79 + 97 is divisible by 64.
