Using binomial theorem compute : (99)^5...

Using binomial theorem compute : `(99)^5`

Text Solution

Verified by Experts

`(99)^{5}=(100-1)^{5}`
`=5_{C_0}(100)^{5}-5_{C_1}(100)^{4}(1)+5_{C_2}(100)^{3}(1)^{2}-5_{C_3}(100)^{2}(1)^{3}+5_{C_4}(100)(1)^{4}-5_{C_5}(1)^{5}`
`=(100)^{5}-5(100)^{4}+10(100)^{3}-10(100)^{2}+5(100)-1`
`=10000000000-500000000+10000000-100000+500-1`
`=10010000500-500100001`
`=9509900499`

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

ARITHMETIC PROGRESSIONS
RD SHARMA|Exercise Solved Examples And Exercises|248 Videos
BRIEF REVIEW OF CARTESIAN SYSTEM OF RECTANGULAR COORDINATES
RD SHARMA|Exercise Solved Examples And Exercises|75 Videos

Similar Questions

Explore conceptually related problems

Using binomial theorem,evaluate: (99)^(5)

Using binomial theorem compute the following: (102)^(6)

Using binomial theorem compute the following: (10.1)65

Using binomial theorem,evaluate: (102)^(5)

Using Binomial theorem, evaluate (0.99)^15 correct to fur places of decimal.

Using binomial theorem,evaluate: (96)^(3)

Derive Binomial theorem

(iv) Using binomial theorem prove that (101)^(^^)50gt(100)^(^^)50+(99)^(^^)50

Using binomial theorem, prove that (101)^(50) gt(100^(50)+99^(50)).

Using binomial theorem,evaluate: (101)^(4)

RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises

Using binomial theorem, expand (x-1/x)^(6)dot
02:41
|
Find an approximation of (0. 99)^5 using the first three terms of its ...
04:17
|
Using binomial theorem compute : (99)^5
02:34
|
Using binomial theorem compute : (102)^6
03:14
|
Using binomial theorem compute : (10. 1)^5
02:40
|
Write down the binomial expansion of (1+x)^(n+1) , when x=8. Deduce th...
04:24
|
Using binomial theorem, prove that 6^n-5n always leaves he remainder 1...
03:05
|
Which is larger (1 0.1)^(100000)\ or 10,000?
03:02
|
If a\ a n d\ b are distinct integers, prove that a^n-b^n is divisible ...
03:21
|
Using binomial theorem, write down the expansion of (2x+3y)^5
03:23
|
Using binomial theorem, write down the expansions of the following: (1...
04:25
|
Using binomial theorem, write down the expansions of the following: ...
04:09
|
Using binomial theorem, write down the expansions of the following: ...
03:55
|
Using binomial theorem, write down the expansions of the following: (2...
02:16
|
Using binomial theorem, write down the expansions of the following: \ ...
02:51
|
Using binomial theorem, write down the expansions of the following: \ ...
06:10
|
Using binomial theorem, write down the expansions of the following: \ ...
03:04
|
Using binomial theorem, write down the expansions of the following: \ ...
03:12
|
Using binomial theorem, write down the expansions of the following:\ (...
02:15
|
Evaluate the following: (sqrt(x+1)+sqrt(x-1))^6+(sqrt(x+1)-sqrt(x-1))^...
05:05
|