Question

# Find the 20th term and the sum of 20 terms of the series : 2×4+4×6+6×8+....

Solution

## Here the nth term of the series is Tn=2n(2n+2) Thus the 20th term will be T20=2×20(2×20+2)=1680 The infinite series can be written as : 2×4+4×6+6×8+...=∑20n−12n(2n+1) Therefore the sum up to 20th term will be =∑20n−12n(2n+1)=∑20n−14n2+∑20n−14n=4∑20n−1n2+4∑20n−1n=4.20(20+1)(2.20+1)6+4.20(20+1)2 =12320MathematicsRD SharmaStandard XI

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