Free Practice Question

PS · Problem Solving

sub-505

Sequences

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

Answer Choices

Correct answer marked below

A

-2010

B

-1

0

Correct

D

1

E

2010

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Sign in Create free account

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

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

Read the full explanation

Sign in for free to see the complete step-by-step solution to this question.

Create free account Sign in

Comments

2

Sign in to join the discussion

Sign in Create free account

T

ThitipongJul 1, 2024

Great explanation

A

AbhilashaJan 20, 2024

Great question!

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.

Unlock full explanations

Create a free account to reveal the correct answer and see step-by-step explanations for every question.

Create free account I already have an account

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