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Deduce a formula (in terms of n) for the following sum: sum (2^i * i) where 1<=i<=n, n,i: natural numbers ( one can write this sum as: 1*2^1+ 2*2^2+ .. +n*2^n)

Let S = sum i* 2 i (i=1,2..n) We multiply this by 2 and we obtain:2S = sum (i 2 i+1 ) = sum [(i+1-1) * 2 i+1 ]= sum[ (i+1) 2 i+1 ] - sum 2 i+1 i=1,2..n ( ) sum (i+1) 2 i+1 = 2 2 2 + .. n 2 n + (n+1)* 2 n+1 =...
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Answered by Alexandru S. • MAT tutor
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What is the square root of the imaginary number i?

Let's suppose that (0+1i) 0.5 = x+iy, where x and y are both real numbers. This is the most general form of a complex number. Now let's square both sides. This gives 0+1i = x 2 +2i xy - y 2 . We will equate ...
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Answered by George D. • MAT tutor
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If a_(n+1) = a_(n) / a_(n-1), find a_2017

We are given; a 1 = 2, a 2 = 6 a n+1 = a n / a n-1 And we want to find a 2017 . The question is hard because if we tried simply applying the formula to get an answer, we would have to do it thousands of time...
TL
Answered by Théodore L. • MAT tutor
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How do you solve hard integration questions using information you know

lets try a few integrations. what is integral of dx/(1+x)? You can see that it is in the form of f'(x)/f(x) so it is ln[f(x)] right? now what about integral of (e^x/(1+e^x))dx that is also in the form of f'(...
DA
Answered by Desmond A. • MAT tutor
1887 Views

How would I go about graph sketching?

You want to look at turning points, intersections and when the gradient is possitive or negative. It is also important to demonstrate what is going on with graphs when they are tending towards 0 (especially ...
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Answered by Simon G. • MAT tutor
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