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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: 12^1+ 22^2+ .. +n*2^n)

Let S = sum i* 2ⁱ (i=1,2..n) We multiply this by 2 and we obtain:2S = sum (i2ⁱ⁺¹ ) = sum [(i+1-1) * 2ⁱ⁺¹ ]= sum[ (i+1)2ⁱ⁺¹ ] - sum 2^i+...

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 = x²
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; a₁ = 2, a₂ = 6 a_n+1 = a_n / a_n-1 And we want to find a₂₀₁₇. The question is hard because if we tried simply applying t...
Answered by Théodore L. • MAT tutor
1975 Views
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 ...
Answered by Desmond A. • MAT tutor
1466 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 (especial...
Answered by Simon G. • MAT tutor
1405 Views
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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: 12^1+ 22^2+ .. +n*2^n)

What is the square root of the imaginary number i?

If a_(n+1) = a_(n) / a_(n-1), find a_2017

How do you solve hard integration questions using information you know

How would I go about graph sketching?

We're here to help

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Search over 10,000 free study notes

Top answers

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)

What is the square root of the imaginary number i?

If a_(n+1) = a_(n) / a_(n-1), find a_2017

How do you solve hard integration questions using information you know

How would I go about graph sketching?

We're here to help

Company Information

Popular Requests

© MyTutorWeb Ltd 2013–2025

CLICK CEOP

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: 12^1+ 22^2+ .. +n*2^n)