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Find the first 3 terms and the sum to infinity of a geometric series with first term, 10 and common ratio 0.2

General form of a Geometric series: a + ar + ar^2 + ar^3 + ar^4 + … First three terms: 10 + 100.2 + 100.2^2 = 10 + 0.2 + 0.04Nth Term of a Geometric Series: ar^n-1 where there are n terms Proof o...

DW
Answered by Daniel W. Maths tutor
7135 Views

Solve the equation 5(2c -3) = 19

Firstly I would try to learn about the students abilities and maybe do an easier linear equations (without brackets) to ensure they have a basic idea how to solve these types of equations. For this questi...

JG
Answered by Jasmine G. Maths tutor
3652 Views

How do you prove the 1^2 +2^2+.....+n^2 = n/6 (n+1) (2n+1) by induction?

There are three simple steps to prove anything by induction.

Step 1: When n=1

12=1

then: 1/6 x 1x (1+1) x (2+1)

=1x2x3/6 =1

Therefore it is true for n=1 

...
VI
Answered by Vaisaalii I. Maths tutor
4571 Views

Express the following as a partial fraction: (4x^2+12x+9) / (x^2+3x+2) .

We first notice that the degree of the numerator is the same as the degree of the denominator so we have an improper fraction which we need to separate into an integer and a proper fraction before we can ...

AP
Answered by Antonia P. Maths tutor
5096 Views

How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?

Split it up into steps:

Step 1: Use compound angle trigonometric formula to re-write Rsin(θ + α)

Since generally sin(θ ± φ) = sinθcosφ ± cosθsinφ

Rsin(θ + α) = R(sinθcosα + cos...

OG
Answered by Oliver G. Maths tutor
12040 Views

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