NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 72
Total: 106
52+62+72 + ..... + 202
Solution:  
The given series can be written in the following way
52+62+72 + ..... + 202 = (12+22+32+...+202) - (12+22+32+42)
=
20
Σ
k=1
k2
4
Σ
k=1
k2
=
20(20+1)(40+1)
6
-
4(4+1)(8+1)
6

=
17220
6
180
6
=
17040
6
= 2840
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