Question

find the sum of 1+2² +3 +4² +5+6² + up to 2n term? please ans fast class 11​

Answer 1

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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