Telescoping sums of reciprocal surd terms by rationalising
This type of question, asked 3 times: CDS 2 2020, CDS 1 2022, CDS 2 2024. All 4 questions below, oldest first.
Try each one first, then open its answer.
Question 1
CDS 2 2020
12What is the value of
1+21+2+31+3+41+…+99+1001 ?
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Question 2
CDS 1 2022
8What is the value of the following?
54+451+65+561+76+671+87+781+98+891
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Question 3
CDS 1 2022
24What is
1+21+2+31+3+41+⋯+2020+20211
equal to?
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Question 4
CDS 2 2024
8What is 10+91+11+101+12+111+…+196+1951 equal to ?
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