Advertisements
Advertisements
Question
Choose the correct alternative:
The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` is
Options
14
7
4
6
Solution
14
APPEARS IN
RELATED QUESTIONS
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`1/(5 + x)`
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`2/(3 + 4x)^2`
Find `root(3)(10001)` approximately (two decimal places
Prove that `root(3)(x^3 + 6) - root(3)(x^3 + 3)` is approximately equal to `1/x^2` when x is sufficiently large
Prove that `sqrt((1 - x)/(1 + x))` is approximately euqal to `1 - x + x^2/2` when x is very small
Write the first 6 terms of the exponential series
e5x
Write the first 6 terms of the exponential series
`"e"^(1/2x)`
Write the first 4 terms of the logarithmic series
`log((1 + 3x)/(1 -3x))` Find the intervals on which the expansions are valid.
Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.
Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 is
Choose the correct alternative:
The coefficient of x8y12 in the expansion of (2x + 3y)20 is
Choose the correct alternative:
If (1 + x2)2 (1 + x)n = a0 + a1x + a2x2 + …. + xn + 4 and if a0, a1, a2 are in AP, then n is
Choose the correct alternative:
If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn − 2Sn−1 + Sn−2 is
Choose the correct alternative:
The sum up to n terms of the series `1/(sqrt(1) +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is
Choose the correct alternative:
The sum of an infinite GP is 18. If the first term is 6, the common ratio is
Choose the correct alternative:
The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is