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Simplify the following expression in the image:
https://ibb.co/5K1GC71
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I made my editing in this post, because THERE IS NO equation in it.
There is an expression, instead, which should be simplified / evaluated.
The starting expression is
S = + + + . . . + - ( + + + . . . + ).
it can be re-grouped as the sum of addends
, n = 1, 2, 3, . . . , 49.
Each addend can be simplified
= = 2n-1.
So, the original sum is the sum of the terms (2n-1), n= 1, 2, 3, . . . 49
1 + 3 + 5 + . . . + 97.
It is the sum of an arithmetic progression with the first term = 1, last term = 97 and the number of terms + 1 = 49.
The sum of this progression is
S = = = = 2401.
ANSWER. The given expression has the value of 2401.
Solved.
(answered by ikleyn,math_tutor2020,Edwin McCravy)