Answer:
15.98
Step-by-step explanation:
∑₁¹⁰
We have to use the formula of sum of a G.P. series with common ratio r < 1.
If the first term is a, the common ratio is r and the number of terms is n then the sum [a + ar + ar² + ar³ + ......... up to n terms] is given by
(Answer)
Answer:
See below
Step-by-step explanation:
Expand L side to get
4n -12 -2n < -10 + 2n simplify L side
2n -12 < -10 +2n subtract 2n from both sides
<u>-12 < -10 </u> <===== so the equation is true for ALL n
(-∞ , + ∞ )
It’d be 2
250 ÷20= 12.5
25 ÷2=12.5
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Step-by-step explanation:
well, the starting equation and the target format have been given.
let's do the multiplications and compare the target with the starting information.
from there we see what is different or missing.
x² + 14x + 13 = 0
and
(x - p)² = q
x² - 2px + p² = q
x² - 2px + (p² - q) = 0
now let's compare the different parts :
x² = x²
-2px = 14x
-2p = 14
p = -7
p² - q = 13
-7² - q = 13
49 - q = 13
36 - q = 0
q = 36
so, the square (x - p)² = (x + 7)² is completed when
x² + 14x + 49 = 0
but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :
x² + 14x + 13 + 36 = 36
x² + 14x + 49 = 36
(x + 7)² = 36
just as we calculated already above.
and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)
x + 7 = ±6
x1 = 6 - 7 = -1
x2 = -6 - 7 = -13