sum of something q (1 Viewer)

Rhanoct

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Find the sum of the first 10 terms of the series 3 + 7 + 13 + ... + [(2^n)+(2n-1)]+...

I was able to find the answer (2146) by finding a to t10 using Tn=[(2^n)+(2n-1)], as there's no common ratio or difference to use the formulas, but what if it asked for the first 100 terms, and it was in an exam? Briefly asked a few friends and they said it could be a combination of AP/GP, but can't find any notes on that in my textbooks.

So yeah... best method = ?

Thanks :)
 

Mark576

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Series: {21 + (2(1)-1), 22 + (2(2)-1), 23 + (2(3)-1) ...}

S10 = S10[AP] + S10[GP] = 10/2[2 + (9)2] + 2(210 - 1)/(2 - 1) = 2146, as required.
 

Rhanoct

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Mark576 said:
Series: {21 + (2(1)-1), 22 + (2(2)-1), 23 + (2(3)-1) ...}

S10 = S10[AP] + S10[GP] = 10/2[2 + (9)2] + 2(210 - 1)/(2 - 1) = 2146, as required.
Ahhhh... I see it.

tyvm
 

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