find the sum of 1+2² +3 +4² +5+6² + up to 2n term? please ans fast class 11
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Answer:
We want to find
Step-by-step explanation:
2
−2
2
+3
2
−4
2
+.... to 2n terms
=1−4+9−16+25−.... to 2n terms
=(1−4)+(9−16)+(25−36)+.... to n terms. (after grouping)
=−3+(−7)+(−11)+....n terms
Now, the above series is in an A.P. with first term a=−3 and common difference d=−4
Therefore, the required sum =
2
n
[2a+(n−1)d]
=
2
n
[2(−3)+(n−1)(−4)]
=
2
n
[−6−4n+4]=
2
n
[−4n−2]
=
2
−2n
(2n+1)=−n(2n+1)
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