Examples
\(\sum_{p=3}^{8}p^2\)
- \(3^{2}= 9\)
- \(4^{2}= 16\)
- \(5^2=25\)
- \(6^2=36\)
- \(7^2=49\)
- \(8^2=64\)
- \(9+16+25+36+49+64 = 199\)
- \(\therefore\) the sum is equal to \(199\)
\(\sum_{r=0}^{5} (7r+1)^2\)
- \((7\times0 +1)^2 = 1\)
- \((7\times{1} +1)^2 = 64\)
- \((7\times{2} +1)^2 = 225\)
- \((7\times{3} +1)^2 = 22^2\)
- \((7\times{4} +1)^2 = 29^2\)
- \((7\times{5} +1)^2 = 36^2\)
Exercise 3A
Q1
a. \(1+3+5+7=16\)
b. Add numbers up to 40: \(1+2+3+\dots+40=820\)
c. Add numbers up to 20: \(1+2+3+\dots+20=210\)
d. Add numbers up to 99: \(1+2+3+\dots+99=\frac{9900}{2}=4950\)
e. Add numbers from 10-40: \(10+11+12+\dots+40=820-45=785\)
f. Add numbers from 100-200: \(100+101+102+\dots+200=20100-4950=15150\)
g. Add numbers from 21 to 40: \(21+22+23+\dots+40=820-210=610\)