Answer: 117
Work Shown
2(2 1/2) +3(2 1/3)+4(2 1/4)+5(2 1/5)+...+10(2 1/10)
= 2(2+1/2) +3(2+1/3)+4(2+1/4)+5(2+1/5)+...+10(2+1/10)
= 2(4/2+1/2) +3(6/3+1/3)+4(8/4+1/4)+5(10/5+1/5)+...+10(20/10+1/10)
= 2(5/2)+3(7/3)+4(9/4)+5(11/5)+...+10(21/10)
= 5+7+9+11+...+21
The last line represents a sum of an arithmetic sequence starting at 5 and common difference 2. Note how 21 = 5+2*(9-1) which shows we're adding 9 terms.
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(1st term + nth term)
S9 = (9/2)*(1st term + 9th term)
S9 = (9/2)*(5 + 21)
S9 = 117
Check:
5+7+9+11+13+15+17+19+21 = 117
The answer is confirmed.