Why should our oceans and how it's being destroyed be talked about more often
Answers
Step by step explanation :-
Here, we have to find out the sum of first 1000 positive integers and the sum of first n positive integers.
★ Solving for first case :-
AP = 1 + 2 + 3 . . . . . . + 1000
Therefore,
n = 1000
l = 1000
a = 1
★ Using formula :-
\qquad\qquad\bf\dag\:\bigg({\sf{\pink{S_{n} = \dfrac{n}{2}\big\lgroup a + l \rgroup}}}\bigg)†(S
n
=
2
n
⎩
⎪
⎧
a+l⟯)
★ Putting all known values :-
\qquad\leadsto\quad\sf S_{1000} = \dfrac{1000}{2}\big\lgroup 1 + 1000\rgroup⇝S
1000
=
2
1000
⎩
⎪
⎧
1+1000⟯
\qquad\leadsto\quad\sf S_{1000} = \dfrac{\cancel{1000}}{\cancel{2}}\big\lgroup 1001\rgroup⇝S
1000
=
2
1000
⎩
⎪
⎧
1001⟯
\qquad\leadsto\quad\sf S_{1000} = 500\:\times\:1001⇝S
1000
=500×1001
\qquad\leadsto\quad{\bf{\purple{S_{1000} = 500500}}}⇝S
1000
=500500
\small\therefore\:{\underline{\sf{Hence,\:sum\:of\:first\:\bf{1000}\:\sf{positive\:integers\:=}\:\bf{500500}}}}∴
Hence,sumoffirst1000positiveintegers=500500
★ Solving for first case :-
AP = 1 + 2 + 3 . . . . . . + n
Therefore,
n = n
l = n
a = 1
★ Using formula :-
\qquad\qquad\bf\dag\:\bigg({\sf{\green{S_{n} = \dfrac{n}{2}\big\lgroup a + l \rgroup}}}\bigg)†(S
n
=
2
n
⎩
⎪
⎧
a+l⟯)