Problem:
2(1−21​)+3(1−31​)+4(1−41​)+…+10(1−101​)=
Answer Choices:
A. 45
B. 49
C. 50
D. 54
E. 55
Solution:
​2(1−21​)+3(1−31​)+4(1−41​)+…+10(1−101​)=2(21​)+3(32​)+4(43​)+…+10(109​)=1+2+3+…+9=45.​
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions