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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 +......
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Answered by Vaisaalii I. • Maths tutor
5080 Views

Is "ser" always used to express something permanent and "estar" for something temporary?

This is a common misconception when learning to distinguish ser and estar. There are many rules and exceptions regarding this. Here's an example: "Mi abuela es mayor" vs "Mi abuela está mayor&...
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Answered by Erlei J. • Spanish tutor
3399 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 exp...
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Answered by Antonia P. • Maths tutor
5599 Views

What is the difference between the perfect tense and the imperfect tense?

Both tenses are used to describe something that happened in the past. In every day conversation, the perfect tense is almost always used e.g. j'ai joué, j'ai trouvé.... When writing, the perfect tense is use...
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Answered by Antoinette C. • French tutor
2382 Views

Explain why benzene is colourless whereas azo dyes (such as methyl yellow) are coloured.

Azo dyes are coloured because they contain alternating single and double bonds, known as a conjugated system. This creates and areas of delocalisation above and below the plane of the molecule. This area of ...
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Answered by Amy S. • Chemistry tutor
44039 Views