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Prove algebraically that (4n + 1)² − (2n − 1) is an even number for all positive integer values of n.

First of all expand the brackets and simplify the expression given:(4n+1)(4n+1)-(2n-1)= 8n2+8n+1-2n+1= 8n2+6n+2= 2(4n2+3n+1). Since the expression can be factorised with 2...

SM
Answered by Shiv M. Maths tutor
10851 Views

dux Gallorum timebat ne Romani viros collem ascendentes audirent. itaque imperavit omnibus Gallis ut in itinere tacerent. ea nocte Galli tam tacite processerunt ut custodes Romani eos non conspicerent.

The leader of the Gauls was afraid that the Romans might hear the men climbing the hill.And so he ordered all the Gauls to say nothing on the journey.That night the Gauls advanced so silently that the Rom...

KM
Answered by Kishan M. Latin tutor
4492 Views

How to recognise and make the link between probability and the algebraic demands of this question?

While I doubt students will ask this exact question, think it provides the basis for what are usually the most difficult questions in GCSE papers, and students would usually be unsure where to start. My i...

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Answered by Neeraj K. Maths tutor
3042 Views

In a circuit with a 12V battery, 20Ω resistor and 10Ω resistor, all in series, calculate the current that would flow?

This question can be split into two parts, the first is calculating overall resistance: in series the Rtotal = R1 + R2 so here Rtotal = 10Ω + 20Ω = 30Ω The seco...

LA
Answered by Lauren A. Biology tutor
5041 Views

How do I remeber the specific elements of a treaty?

I find it easiest to remember the different elements of a treaty by creating an acronomyn. For example, the Treaty of Versailles angered many germans due to four clauses. Loss of territories, limitations ...

LM
Answered by Lucinda M. History tutor
2748 Views

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