For non zero real numbers a and b. define a\timesb= \frac{1}{a}+ \frac{1}{b}.Then \sum_{k=1}^{10}(1\times \frac{1}{k})=

AP ICET 2017 Shift 1 Paper

Question : 73 of 200

Marks: +1, -0

For non zero real numbers a and b. define

a×b=\;\;{1}/{a}+\;\;{1}/{b}

.Then

∑_{k=1}^{10}(1×\;\;{1}/{k})=

Solution:

Since a × b is defined as

1/a+1/b

, we can write

1×{1}/{k}=1+k

∑↙{k=1}↖{10}(1+k)=2+3+4+. . .+11

This is an A.P. with

n=10,a=2,d=1

{S}_{n}={n}/{2}[2a+(n-1)d]=5(4+9×1)=65

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