January 2021
Problem of the Month

Interesting Sums
Submitted by Brijesh Dave

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 + ... + 15 + 17 =
(H)   1 + 3 + 5 + 7 + ... + 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 + ... + 17 = 81
(H)   1 + 3 + 5 + 7 + ... + 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

Send any comments or questions to: David Pleacher