The value of 1^3-2^3+3^3-4^3+-14^3+15^3 is:

Question

The value of $1^3-2^3+3^3-4^3+\cdots-14^3+15^3$ is:

Accepted Answer

Group in pairs, leaving $15^3$ alone: $(1^3-2^3)+(3^3-4^3)+\cdots+(13^3-14^3)+15^3$.

$$1^3-2^3=-7,\ 3^3-4^3=-37,\ 5^3-6^3=-91,\ 7^3-8^3=-169,\ 9^3-10^3=-271,\ 11^3-12^3=-397,\ 13^3-14^3=-547.$$

Sum of these seven negative terms $=-(7+37+91+169+271+397+547)=-1519$.

$$\text{Total}=15^3-1519=3375-1519=1856.$$

Solutions · 1