Question

use Gauss's approach to find the following sums (do not use formulas).

a. 1+2+3+4+...+98
b. 1+3+5+7+...+997

a. the sum of the sequence is?

Answer 1

after solving for a it will want u to solve for b i dont understand it at all though.

Answer 2

isnt this where you just reverse the order and add them together?\[Sum=1+2+\cdots +97+98\]\[Sum=98+97+\cdots+2+1\]adding them gives:
\[2\cdot Sum=(1+98)+(2+97)+\cdots + (97+2)+(98+1)\]\[\iff 2\cdot Sum = \underbrace{99+99+\cdots +99+99}_{\frac{98}{2} \mbox \times}\]
\[\iff 2\cdot Sum = 99\cdot 98\iff Sum = \frac {99\cdot 98}{2}\]

Answer 3

oops, that should be "98 times" under the bracket.

Answer 4

so is this easy but they make it look complicateted?

Answer 5

i guess o.O its easy for some but not easy for all.

Answer 6

how would i solve for the second one?