NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 83
Total: 106
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Solution:
The numbers from 1 to 100 which are divisible by 2 or 5 are 2, 4, 5, 6, 8, 10, 12, 14, 15, ....., 95, 96, 98, 100.
∴ Required sum = 2 + 4 + 5 + 6 + 8 + 10 + ..... + 95 + 96 + 98 + 100
= (2 + 4 + 6 + 8 + 10 + ..... + 96 + 98 + 100) + (5 + 15 + 25 + ...... + 95)
= 2(1 + 2 + 3 + ...... + 50) + 5 (1 + 3 + 5 + ..... + 19)
= 2
k + 5 n 2
Since Sum of first n odd natural numbers isn 2
= 2
+ 5 ( 10 ) 2 = (50 × 51) + (5 × 100) = 2550 + 500 = 3050
∴ Required sum = 2 + 4 + 5 + 6 + 8 + 10 + ..... + 95 + 96 + 98 + 100
= (2 + 4 + 6 + 8 + 10 + ..... + 96 + 98 + 100) + (5 + 15 + 25 + ...... + 95)
= 2(1 + 2 + 3 + ...... + 50) + 5 (1 + 3 + 5 + ..... + 19)
= 2
Since Sum of first n odd natural numbers is
= 2
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