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Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the ...

Answered by Carlo M. • Maths tutor

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Find the area under the curve of f(x)=4x/(x^2+1) form x = 0 to x = 2.

Solution of all integration problems starts with investigation of a given function. We can’t represent it with standard functions, i.e. linear, power or trigonometric. Second step would be to try substitu...

Answered by Igors D. • Maths tutor

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Why a sodium ion has a smaller radius than a sodium atom?

Let’s look closer at the sodium atom. Really close, so we could see. Atom is a neutral species, with 11 protons in the nucleus. We can find that information in the periodic table. 11 proton charge should ...

Answered by Igors D. • Chemistry tutor

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How can different phenotypes be generated without changes to the genotype?

Different phenotypes can be generated without changes to the genotype through a process called Epigenetics. Epigenetics, meaning “above genes”, is the study of changes to the phenotype caused by changes i...

Answered by Ana D. • Biology tutor

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