Alan

If you want log to the base e use ln instead of log.  If you want another base use log(x,b) where b is the base and x is the number of which you want the log.

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This graph should help you to be confident!

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There is no solution! See above. Are you sure you've written the equation correctly?

Form the average of a finite sum over n, then take the limit as n tends to infinity.  Examples:

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And:

See views below

"What number do you need to divide 55 by to get (-11)"

55/x = -11

x = 55/(-11)

x = -5

It's always possible to find another number in any sequence!  For example, consider the function:

f(n) = - (19/6)n⁴ + (175/6)n³ - (235/3)n² + (421/3)n - 9

n        f(n)

1          79

2        141

3        238

4        355

5        401

6        209

Of course, this might not be the sequence the questioner had in mind!

A)  therre are 13 clubs in 52 cards so the probability of drawing a club is 1/4.  Since there are four independent decks involved here the probability of all four drawing a club is (1/4)⁴, or 1/256

B).  There are 26 red cards in a deck, so probability of drawing one is 26/52 or 1/2

      There are 4 kings in a deck, so probability of drawing one is 4/52 or 1/13

      There are 26 black cards, so probability of drawing one is 1/2

      There is only one 2 of clubs so probability of drawing it is 1/52

Overall probability is obtained by multiplying these together, namely:  (1/2)*(1/13)*(1/2)*(1/52) or 1/2704

C) Try this one yourself using a similar sort of reasoning.

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We have  \((x+y)^2=x^2+y^2+2xy\)

So  \(x^2+y^2=(x+y)^2-2xy\)

Here:  \(x^2+y^2=5^2-2(-3)\text{ ... or ... }x^2+y^2=25+6\rightarrow31\)

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