Calculate the sum of the series (-1)^1 + (-1)… | GMAT Sprint

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PS · Problem Solving

sub-505

Sequences

Calculate the sum of the series $(-1)^1 + (-1)^2 + ... + (-1)^{2010}$ .

Answer Choices

Correct answer marked below

-2010

-1

Correct

2010

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Explanation

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Official Explanation

Official

In this series, the last term has an exponent of 2010, which is even. Therefore, the sum of the series…

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Comments

ThitipongJul 1, 2024

Great explanation

AbhilashaJan 20, 2024

Great question!

VanessaAug 27

is it just alternating -1 and 1? so they cancel out?

UjjawalSep 1

wait what if it was odd number of terms? then it wouldn't cancel the same way right

AdyantSep 3

right, the last term would be left over. good thing 2010 is even here

RitikMay 21

thanks, this one was quick 🙂

MarcosAug 10

easy points if you just notice the pattern. even exponent = 1, odd = -1

AniketApr 19

huh i overthought this and started trying to use a formula lol. sometimes just look at the pattern

AndreaApr 23

lol classic. sequences questions love to trick you into doing too much work

What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

Calculate the sum of the series (−1)1+(−1)2+...+(−1)2010(-1)^1 + (-1)^2 + ... + (-1)^{2010}(−1)1+(−1)2+...+(−1)2010.