find the value of 1/1+√2 +1/√2+√3+1/√3+√4.......+1/√8+√9
Answers
Answered by
6
1÷(1+√2)=(2–1)÷(1+√2)=√2–1
1÷(√2+√3)=(3–2)÷(√2+√3)=√3-√2
1÷(√3+√4)=(4–3)÷(√3+√4)=√4-√3
Similarly for the other terms upto 99
Therefore sum of the given series upto ’n’ terms is equal to √(n+1)-1 bco it becomes telescope series
Hence sum of the series upto 99 terms is √100–1=10–1=9.
1÷(√2+√3)=(3–2)÷(√2+√3)=√3-√2
1÷(√3+√4)=(4–3)÷(√3+√4)=√4-√3
Similarly for the other terms upto 99
Therefore sum of the given series upto ’n’ terms is equal to √(n+1)-1 bco it becomes telescope series
Hence sum of the series upto 99 terms is √100–1=10–1=9.
Similar questions