Advertisements
Advertisements
Question
Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is
Options
`("n"("n" - 1))/2`
`("n"("n" + 1))/2`
`(2"n"(2"n" + 1))/2`
n(n + 1)
Solution
n(n + 1)
APPEARS IN
RELATED QUESTIONS
Evaluate the following using binomial theorem:
(999)5
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the middle terms in the expansion of
`(3x + x^2/2)^8`
Find the term independent of x in the expansion of
`(x^2 - 2/(3x))^9`
Find the term independent of x in the expansion of
`(2x^2 + 1/x)^12`
Show that the middle term in the expansion of is (1 + x)2n is `(1*3*5...(2n - 1)2^nx^n)/(n!)`
The constant term in the expansion of `(x + 2/x)^6` is
Compute 1024
Compute 994
Compute 97
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Find the coefficient of x2 and the coefficient of x6 in `(x^2 -1/x^3)^6`
Find the coefficient of x4 in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`
Find the last two digits of the number 3600
If a and b are distinct integers, prove that a − b is a factor of an − bn, whenever n is a positive integer. [Hint: write an = (a − b + b)n and expaand]
In the binomial expansion of (1 + x)n, the coefficients of the 5th, 6th and 7th terms are in AP. Find all values of n
Choose the correct alternative:
The remainder when 3815 is divided by 13 is