sum of something q (1 Viewer)

[Rhanoct]

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]

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.

 

[ticky2002]

I can't remember any of this stuff

 

[Rhanoct]

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