Determine each of the following sums:

(A)   1 + 3 + 5 =
(B)   1 + 3 + 5 + 7 =
(C)   1 + 3 + 5 + 7 + 9 =
(D)   1 + 3 + 5 + 7 + 9 + 11 =
(E)   1 + 3 + 5 + 7 + 9 + 11 + 13 =
(F)   1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 =
(G)   1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =
(H)   1 + 3 + 5 + 7 + ... + 291 + 293 + 295 =
(I)   1 + 3 + 5 + 7 + 9 + 11 + 13 + ... + R =

Solution to the Problem:

(A)   1 + 3 + 5 = 9
(B)   1 + 3 + 5 + 7 = 16
(C)   1 + 3 + 5 + 7 + 9 = 25
(D)   1 + 3 + 5 + 7 + 9 + 11 = 36
(E)   1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
(F)   1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
(G)   1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
(H)   1 + 3 + 5 + 7 + ... + 291 + 293 + 295 =
        ( (1 + 295) / 2)2 = 21,904
(I)   1 + 3 + 5 + 7 + 9 + 11 + 13 + ... + R =
        ( (1 + R) / 2)2

Ivy Joseph sent in a different answer for (I): ([R/2] + 1)2 which also works.

Correctly solved by:

1. Brijesh Dave Mumbai City, Maharashtra, India
2. Colin (Yowie) Bowey Beechworth, Victoria, Australia
3. Veena Mg Bangalore, Karnataka, India
4. Ivy Joseph Pune, Maharashtra, India
5. Taylor Balding Redlands Middle School
Grand Junction, Colorado