16. (1) Find the sum of first 1000 positive integers.
Answers
Answer:
The number series 1, 2, 3, 4, . . . . , 999, 1000. Therefore, 500500 is the sum of positive integers upto 1000.
500500
Answer:
50050
Step-by-step explanation:
Complete step-by-step answer:
The positive integers start from 1.
The series of the positive integers starting from 1, and
end at 1000 is shown below.
\[1,2,3,4,5, \ldots \ldots,1000 \]
The total number of terms \[n\] in the series are 1000. First number \[a\] of the series is 1 and the common
difference V[d\] is 1.
The formula for the sum \[S\] of \[n\] terms in A.P. is
shown below.
V[S = \dfrac{n}{2}\left\{{2a + \left( {n - 1} \right)d} \right\}
Substitute 1000 for\[n\], 1 for \[a\] and for \[d\] in the
above equation.
WWWS = \dfrac{{1000}}{2}\left\{ {2\left( 1 \right) + \left(
{1000 - 1} \right)1} \right\} \\
\rightarrow S = 500\left\{ {2+ 999} \right\} \\ \Rightarrow S = 500\left\{{1001} \right\} \\
\Rightarrow S = 500500 \\