Question

Use Gauss's approach to find the following sums. (Do not use formulas.) a. 1+2+3+4+...+99 b. 1+3+5+7+...+103

Answer 1

i don't know Gauss approach.
1+2+3+............97+98+99
=(1+99)+(2+98)+(3+97)+(4+96)+.....+(48+52)+(49+51)+50
=100*49+50=4950

Answer 2

Okay thank you so much! I am not very good at Math and did not understand.

Answer 3

I need the sum of a, and b

Answer 4

i have not used formula ,only arranged the terms.

Answer 5

first term goes on increasing second goes on decreasing.

Answer 6

b.
1+3+5+...+99+101+103
=1+2+3+...+99-(2+4+6+...+98)+101+103
=4950-2(1+2+3+...+49)+204
=4950-2{(1+49)+(2+48)+(3+47)+...+(23+27)+(24+26)+25}+204
=4950-2(50*24+25)+204
=4950-2*1225+204
=4950-2450+204
=2500+204
=2704