Home
Class 12
MATHS
The value of 99^(50) - 99.98^(50) + (99...

The value of ` 99^(50) - 99.98^(50) + (99*98)/(1*2) (97)^(50) -…+ 99 ` is

A

`0`

B

`-1`

C

`-2`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `99^(50)-99.98^(50)+(99.98)/(1.2)(97)^(50)-....+99`
`=^(99)C_(0)99^(50)-^(99)C_(1)(99-1)^(50)+^(99)C_(2)(99-2)^(50)-....+^(99)C_(98)(99-98)^(50)+^(99)C_(99)(99-99)^(50)`
`=99^(50)('^(99)C_(0)-^(99)C_(1)+^(99)C_(2)-^(99)C_(3)+...)+^(50)C_(1)*99^(49)('^(99)C_(1)-2*^(99)C_(2)+3*^(99)C_(3)-....)+....`
`=0+0+0+....+0=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

find the value of (99)^4 .

find tha value of (99)^3 .

An equation a_(0) + a_(2)x^(2) + "……" + a_(99)x^(99) + x^(100) = 0 has roots .^(99)C_(0), .^(99)C_(1), ^(99)C_(2), "…..", .^(99)C_(99) The value of (.^(99)C_(0))^(2) + (.^(99)C_(1))^(2) + "….." + (.^(99)C_(99))^(2) is equal to

The value of sum_(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C_(r)) is "_____" .

Which is larger : (99^(50)+100^(50)) or (101)^(50) .

Show that 101^(50)gt 99^(50)+100^(50)

If H_n=1+1/2+...+1/ndot , then the value of S_n=1+3/2+5/3+...+(99)/(50) is a. H_(50)+50 b. 100-H_(50) c. 49+H_(50) d. H_(50)+100

Fill in the blank: The value of int_(-1)^(1)(1+x+3x^(3)+5x^(5)+…+99x^(99))dx is ___________.

Evaluate: 1+i^99+i^100

Find the value of 4tan^(-1)(1/5)-tan^(-1)(1/(70))+tan^(-1)(1/(99))