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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 + 10 0.2 + 10 0.2^2 = 10 + 0.2 + 0.04Nth Term of a Geometric Series: ar^n-1 where there are n terms Proof of sum of t...
DW
Answered by Daniel W. • Maths tutor
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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 1 2 =1 then: 1/6 x 1x (1+1) x (2+1) =1x2x3/6 =1 Therefore it is true for n=1 Step 2: Assume it is true for n=k so, 1 2 + 2 2 +......
VI
Answered by Vaisaalii I. • Maths tutor
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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 exp...
AP
Answered by Antonia P. • Maths tutor
5703 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 + cosθsinα) = Rsinθcosα + Rcosθsinα ...
OG
Answered by Oliver G. • Maths tutor
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Calculate the distance of the centre of mass from AB and ALIH of the uniform lamina.

The diagram shows the lamina shape. To begin, divide the lamina into smaller sections and calculate the area. In this example, the lamina is best divided into sections A, B and C. Calculate the areas. For ex...
CS
Answered by Chandler S. • Maths tutor
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