Question

Sum of series(1+2)+(3+5)+(6+7)+(9+10)+....+(93+94)++95+97)+(98+99) will be

Answer 1

Given: The series (1+2)+(3+5)+(6+7)+(9+10)+....+(93+94)++95+97)+(98+99)

To find: Sum of series.

Solution:

• Now the series given is:

                  S =  (1+2)+(3+5)+(6+7)+(9+10)+....+(93+94)++95+97)+(98+99)

• We can write it as:

                  S = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ......+ 100) - ( 4 + 8 + 12 + 16 + ...... + 100 )

• Now second series is an AP.

• Sum of natural numbers is: n(n+1) / 2

• So applying that, we get:

                  100 x 101 / 2 - 4(1 + 2 + + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...... 25)

                  5050 - 4(25+26 / 2)

                  5050 - 1300

                  3750

Answer:

               So the sum of the series is 3750.

Answer 2

Answer:

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