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What is the sum of the infinite geometric series 1 + 1/3 + 1/9 +1/27 ...?

An infinite geometric series is of the form a*(1 + b + b^2 + b^3 ...)

To find the sum of all the terms in this series we consider the sum, S, where:

S= 1 + b + b^2 + b^3 ... + b^n

whe...

Answered by Ryan T. • Maths tutor

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Using partial fractions find the integral of (15-17x)/((2+x) (1-3x)^2 )

First seperate the function into the form A/(2+x) + B/(1-3x) + C/(1-3x)² . Find A B and C by equating the intergral to {A(1-3x)²+B(1-3x)(2+x) +C(2+x)}/(2+x)(1-3x)²

Answered by Sean B. • Maths tutor

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how do you differentiate tan(x)

The differential of tan(x) is sec²(x), however knowing how dy/dx tan(x)=sec²(x) is very useful in differentiating other trigonometric functions. So, if we first employ the rule that ...

Answered by Olukorede S. • Maths tutor

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Solve the simultaneous equation: y+4x+1=0 y^2+5x^2+2x=0

Rearrange the first equation to get y on its own: y=-(1+4x) Substitute into the second equation: (1+4x)(1+4x)+5x^2+2x=0 21x^2+10x+1=0 Substite into the quadratic formula to solve (-b+/-(b^...

Answered by George L. • Maths tutor

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a) Simplify 2ln(2x+1) - 10 = 0 b) Simplify 3^(x)*e^(4x) = e^(7)

a) To answer this question, one must be familiar with laws of logs, more sprecifically the rules when applied to the natural log of x, and exponentials (e). 2ln(2x+1) - 10 = 0 Step 1) 2ln(2x+1) = 10 Step ...

Answered by Jordan B. • Maths tutor

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