SOLUTION: If the sum of n terms of a series is 2n^2+3n+4. Find the series and also its nth term.

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Question 1012112: If the sum of n terms of a series is 2n^2+3n+4. Find the series and also its nth term.
Answer by ValorousDawn(53)   (Show Source): You can put this solution on YOUR website!
If f(n) is a function that gives you the sum of the first n terms, the nth term is given by subtracting away the previous terms. Since terms are integers apart (1,2,3), we can extract the nth term by taking the sum to n, and subtracting away the sum of n-1. Thus, n=f(n)-f(n-1).
Solved by pluggable solver: EXPLAIN simplification of an expression
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YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: 2n^2+3n+4-2*(n-1)^2+3*(n-1)+4 simplifies to 2*n^2+6*n-2*(n-1)^2+5
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 2n^2+3n+4-2*(n-1)^2+3*(n-1)+4 )
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DETAILED EXPLANATION

Look at .
Added fractions or integers together
It becomes .
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Moved 8 to the right of expression
It becomes .
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Expanded term 3 by using associative property on %28n-1%29
It becomes .
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Multiplied numerator integers
It becomes .
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Added fractions or integers together
It becomes .
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Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+3%2An+%29 replacing them with highlight_green%28+%283%2B3%29%2An+%29
It becomes .
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Added fractions or integers together
It becomes .
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Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!
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